Problem library

Find a problem

Search by course or topic.

Search problems

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Numerical Methods are shortened. Search still covers every problem.

More filters

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Clear

Browsing still works.Sign in to add progress, saved problems and private labels.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsBuild a practice set

NUM:010217A bisection count is a width certificate, not a residual test

View access options

Num Bisection Width CertificateNum Ivt Uniqueness Enclosure

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010218Secant through two values is superlinear and is not Newton's tangent

View access options

Num Secant Interpolant UpdateNum Secant Order Versus Newton

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010219A fixed-point rearrangement is useless unless it contracts on an invariant interval

View access options

Num Contraction Mapping Invariant IntervalNum Picard Apriori Bound

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010324Two conjugate-gradient steps close an SPD two-by-two residual

View access options

Num CG Exact IterationNum CG A Orthogonality Finite Termination

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010325Two Householder reflectors expose a least-squares residual

View access options

Num Householder Reflector QRNum QR Least Squares Residual Projection

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010326An isolated Gershgorin disk names the target of power iteration

View access options

Num Gershgorin IsolationNum Power Iteration Rayleigh Quotient

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010420Matching values and derivatives needs repeated-node divided differences

View access options

Num Hermite Repeated Node Divided DifferencesNum Hermite Remainder Identity

PrivateLabels unavailable

Private saving unavailable

Interpolation and approximationNumerical Methods · Mixed review

Progress not loaded

NUM:010421Natural end conditions make a cubic spline, not the interpolating quadratic

View access options

Num Natural Cubic Moment SystemNum Spline Evaluation Versus Polynomial

PrivateLabels unavailable

Private saving unavailable

Interpolation and approximationNumerical Methods · Mixed review

Progress not loaded

NUM:010522Two Gauss nodes integrate cubics exactly and miss a concrete quartic

View access options

Num Gauss Legendre Nodes WeightsNum Gauss Legendre Degree Error Audit

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010523A trapezoid Romberg triangle recovers the integral of a fifth power

View access options

Num Romberg Trapezoid TableNum Richardson Even Powers Exactness

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010531A Monte Carlo mean is unbiased, but Chebyshev still buys the sample size

View access options

Num Monte Carlo Unbiased VarianceNum Chebyshev Sample Size Certificate

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010627One classical RK4 step is fifth-order locally and fourth-order globally

View access options

Num Rk4 Stage ArithmeticNum Onestep Local Versus Global Order

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010628An AB2 predictor needs a second value before the AM2 corrector can start

View access options

Num Adams Interpolant DerivationNum Pece Starting Value Audit

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010629Linear shooting hits the far boundary in one sensitivity step

View access options

Num Linear Shooting Two IvpNum Sensitivity Newton For Missing Slope

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010630A two-node Poisson grid makes truncation visible and quadratics exact

View access options

Num Centered Difference TruncationNum Small Grid Poisson Solve

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922011In a floating-point system with unit roundoff u, a computed approximation \hat{y} to y = f(x) is said to be accurat…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922012Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922013A 6-digit decimal chopping floating-point system is used to compute x - y with x = 0.314159 \times 10^{1} and y = 0…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922014Let x be a positive normalized machine number and let \oplus,\otimes denote floating-point addition and multiplicat…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922015The function f(x) = \frac{1-\cos x}{x^2} for x \ne 0, with f(0) := 1/2, is to be evaluated for small x.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922016Classification.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922017Let \mathrm{fl}(\cdot) denote rounding to nearest in a binary floating-point system with precision t \ge 2 and unit…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922018Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922019A quantity y is computed from data x by an algorithm that is backward stable: the computed \hat{y} is the exact f(\…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922020In four-digit decimal floating-point arithmetic with rounding to nearest, compute \mathrm{fl}(a+b) and \mathrm{fl}(…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922021Let f(x) = \tan x near x = \pi/2.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922022Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922023A binary floating-point system has subnormals: numbers of the form \pm 0.d_1 d_2 \ldots d_{t-1} \times 2^{e_{\min}}…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922024Let c(x) = \cos x and s(x) = \sin x be evaluated by library functions satisfying |\mathrm{fl}(c(x)) - \cos x| \le u…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922025The sample variance of machine numbers x_1,\ldots,x_n may be computed by or by the two-pass formula s^2 = \frac{1}{…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922026Prove that in any floating-point system with base \beta \ge 2, precision t \ge 1, and rounding to nearest (ties bro…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922027Let f(x) = \frac{e^{x}-1}{x} for x \ne 0, f(0) := 1.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922028Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922029A complex number z = x+iy with machine-real x,y is multiplied by w = u+iv using the formula (xu-yv)+i(xv+yu).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922030Let \{x_k\}_{k=0}^{n} be machine numbers and let p(t) = \prod_{k=0}^{n} (t-x_k).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922031Let f(x)=x^3-2x-5.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922032Let f be continuous on [a,b] with f(a)f(b)<0, and suppose f has exactly one root r\in(a,b).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922033Consider f(x)=\mathrm{e}^{-x}-x.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922034Apply Newton's method to f(x)=x^2-2 with initial guess x_0=1.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922035Let f be twice continuously differentiable on an open interval containing a simple root r, so that f(r)=0 and f'(r)…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Problem library

Find a problem

Search by course or topic.

Search problems

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Numerical Methods are shortened. Search still covers every problem.

More filters

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Clear

Browsing still works.Sign in to add progress, saved problems and private labels.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsBuild a practice set

NUM:010217A bisection count is a width certificate, not a residual test

View access options

Num Bisection Width CertificateNum Ivt Uniqueness Enclosure

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010218Secant through two values is superlinear and is not Newton's tangent

View access options

Num Secant Interpolant UpdateNum Secant Order Versus Newton

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010219A fixed-point rearrangement is useless unless it contracts on an invariant interval

View access options

Num Contraction Mapping Invariant IntervalNum Picard Apriori Bound

PrivateLabels unavailable

Private saving unavailable

Root finding and nonlinear systemsNumerical Methods · Mixed review

Progress not loaded

NUM:010324Two conjugate-gradient steps close an SPD two-by-two residual

View access options

Num CG Exact IterationNum CG A Orthogonality Finite Termination

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010325Two Householder reflectors expose a least-squares residual

View access options

Num Householder Reflector QRNum QR Least Squares Residual Projection

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010326An isolated Gershgorin disk names the target of power iteration

View access options

Num Gershgorin IsolationNum Power Iteration Rayleigh Quotient

PrivateLabels unavailable

Private saving unavailable

Linear systems, least squares, and eigenproblemsNumerical Methods · Mixed review

Progress not loaded

NUM:010420Matching values and derivatives needs repeated-node divided differences

View access options

Num Hermite Repeated Node Divided DifferencesNum Hermite Remainder Identity

PrivateLabels unavailable

Private saving unavailable

Interpolation and approximationNumerical Methods · Mixed review

Progress not loaded

NUM:010421Natural end conditions make a cubic spline, not the interpolating quadratic

View access options

Num Natural Cubic Moment SystemNum Spline Evaluation Versus Polynomial

PrivateLabels unavailable

Private saving unavailable

Interpolation and approximationNumerical Methods · Mixed review

Progress not loaded

NUM:010522Two Gauss nodes integrate cubics exactly and miss a concrete quartic

View access options

Num Gauss Legendre Nodes WeightsNum Gauss Legendre Degree Error Audit

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010523A trapezoid Romberg triangle recovers the integral of a fifth power

View access options

Num Romberg Trapezoid TableNum Richardson Even Powers Exactness

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010531A Monte Carlo mean is unbiased, but Chebyshev still buys the sample size

View access options

Num Monte Carlo Unbiased VarianceNum Chebyshev Sample Size Certificate

PrivateLabels unavailable

Private saving unavailable

Numerical differentiation and quadratureNumerical Methods · Mixed review

Progress not loaded

NUM:010627One classical RK4 step is fifth-order locally and fourth-order globally

View access options

Num Rk4 Stage ArithmeticNum Onestep Local Versus Global Order

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010628An AB2 predictor needs a second value before the AM2 corrector can start

View access options

Num Adams Interpolant DerivationNum Pece Starting Value Audit

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010629Linear shooting hits the far boundary in one sensitivity step

View access options

Num Linear Shooting Two IvpNum Sensitivity Newton For Missing Slope

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

NUM:010630A two-node Poisson grid makes truncation visible and quadratics exact

View access options

Num Centered Difference TruncationNum Small Grid Poisson Solve

PrivateLabels unavailable

Private saving unavailable

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922011In a floating-point system with unit roundoff u, a computed approximation \hat{y} to y = f(x) is said to be accurat…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922012Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922013A 6-digit decimal chopping floating-point system is used to compute x - y with x = 0.314159 \times 10^{1} and y = 0…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922014Let x be a positive normalized machine number and let \oplus,\otimes denote floating-point addition and multiplicat…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922015The function f(x) = \frac{1-\cos x}{x^2} for x \ne 0, with f(0) := 1/2, is to be evaluated for small x.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922016Classification.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922017Let \mathrm{fl}(\cdot) denote rounding to nearest in a binary floating-point system with precision t \ge 2 and unit…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922018Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922019A quantity y is computed from data x by an algorithm that is backward stable: the computed \hat{y} is the exact f(\…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922020In four-digit decimal floating-point arithmetic with rounding to nearest, compute \mathrm{fl}(a+b) and \mathrm{fl}(…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922021Let f(x) = \tan x near x = \pi/2.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922022Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922023A binary floating-point system has subnormals: numbers of the form \pm 0.d_1 d_2 \ldots d_{t-1} \times 2^{e_{\min}}…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922024Let c(x) = \cos x and s(x) = \sin x be evaluated by library functions satisfying |\mathrm{fl}(c(x)) - \cos x| \le u…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922025The sample variance of machine numbers x_1,\ldots,x_n may be computed by or by the two-pass formula s^2 = \frac{1}{…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922026Prove that in any floating-point system with base \beta \ge 2, precision t \ge 1, and rounding to nearest (ties bro…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922027Let f(x) = \frac{e^{x}-1}{x} for x \ne 0, f(0) := 1.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922028Honors.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922029A complex number z = x+iy with machine-real x,y is multiplied by w = u+iv using the formula (xu-yv)+i(xv+yu).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922030Let \{x_k\}_{k=0}^{n} be machine numbers and let p(t) = \prod_{k=0}^{n} (t-x_k).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922031Let f(x)=x^3-2x-5.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922032Let f be continuous on [a,b] with f(a)f(b)<0, and suppose f has exactly one root r\in(a,b).

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922033Consider f(x)=\mathrm{e}^{-x}-x.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922034Apply Newton's method to f(x)=x^2-2 with initial guess x_0=1.

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

NUM:9922035Let f be twice continuously differentiable on an open interval containing a simple root r, so that f(r)=0 and f'(r)…

View access options

Error ConditioningNumerical Methods Problem Solving

PrivateLabels unavailable

Private saving unavailable

Floating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation

Progress not loaded

Problem results

NUM:9922001A decimal floating-point system uses base \beta = 10, precision t = 4, and exponent range -2 \le e \le 3.

NUM:9922002In IEEE-style binary floating-point with base \beta = 2, precision t, and rounding to nearest (ties to even), the u…

NUM:9922003A binary floating-point format has a 1-bit sign, an 8-bit exponent stored with bias 127, and a 23-bit stored fracti…

NUM:9922004Let \varepsilon_{\mathrm{mach}} be the machine epsilon of a rounding-to-nearest binary floating-point system.

NUM:9922005Suppose all elementary operations are performed in floating-point arithmetic satisfying \mathrm{fl}(a \odot b) = (a…

NUM:9922006Let f(x) = \sqrt{1+x}-1 for x > -1.

NUM:9922007The quadratic equation ax^2 + bx + c = 0 with a \ne 0 has roots when b^2-4ac \ge 0.

NUM:9922008Define the absolute condition number of a differentiable scalar function f at x by \kappa_{\mathrm{abs}}(x) = |f'(x…

NUM:9922009Consider evaluating p(x) = x^2 - 2x + 1 at machine numbers near x = 1.

NUM:9922010Let A be an invertible n \times n real matrix and b \in \mathbb{R}^n.

Find a problem

Problem results

NUM:9922001A decimal floating-point system uses base \beta = 10, precision t = 4, and exponent range -2 \le e \le 3.

NUM:9922002In IEEE-style binary floating-point with base \beta = 2, precision t, and rounding to nearest (ties to even), the u…

NUM:9922003A binary floating-point format has a 1-bit sign, an 8-bit exponent stored with bias 127, and a 23-bit stored fracti…

NUM:9922004Let \varepsilon_{\mathrm{mach}} be the machine epsilon of a rounding-to-nearest binary floating-point system.

NUM:9922005Suppose all elementary operations are performed in floating-point arithmetic satisfying \mathrm{fl}(a \odot b) = (a…

NUM:9922006Let f(x) = \sqrt{1+x}-1 for x > -1.

NUM:9922007The quadratic equation ax^2 + bx + c = 0 with a \ne 0 has roots when b^2-4ac \ge 0.

NUM:9922008Define the absolute condition number of a differentiable scalar function f at x by \kappa_{\mathrm{abs}}(x) = |f'(x…

NUM:9922009Consider evaluating p(x) = x^2 - 2x + 1 at machine numbers near x = 1.

NUM:9922010Let A be an invertible n \times n real matrix and b \in \mathbb{R}^n.