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ProblemsClear skill: Nonlinear Equations Build a practice set

ProblemCourse & topicStatus

NUM:9922051Let g be continuously differentiable on an open interval containing a fixed point r=g(r), and assume |g'(r)|<1.

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922052Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922053Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922054Consider bisection on a continuous f with a unique root in [a,b].

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

—

NUM:9922055Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922056Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

—

NUM:9922057Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

—

NUM:9922058Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

—

NUM:9922059A floating-point implementation of Newton's method for a simple root uses the combined stopping rule: halt at the…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922060Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

—

NUM:9922061Apply Gaussian elimination without pivoting to the linear system…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922062Let A\in\mathbb{R}^{n\times n} be nonsingular and suppose Gaussian elimination without pivoting produces the…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922063Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922064Perform LU factorization without pivoting on…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922065Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922066Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922067Let PA=LU be the PA=LU factorization of a nonsingular matrix A\in\mathbb{R}^{n\times n} obtained by Gaussian…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922068Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922069Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922070Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922071Derive the multipliers and the reduced upper-triangular matrix produced by one full step of Gaussian elimination…

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922072Let A\in\mathbb{R}^{n\times n} have the LU factorization A=LU without pivoting.

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922073Mathematical problem title

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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NUM:9922074A square matrix A is said to be strictly diagonally dominant if |a_ii|>\sum_{j\neq i}|a_ij| for every row index i.

Nonlinear EquationsNumerical Methods Problem Solving

Root finding and nonlinear systemsNumerical Methods · Calculation

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Showing 24 of 50 matching problems.

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Apply one step of Newton's method, one step of the secant method, and one step of false position to

f(x)=\sin

…

Let

f(x)=x\mathrm{e}^{x}-1

.

The modified Newton iteration for a root of known integer multiplicity

m\ge 2

is…

Let

f

be twice continuously differentiable near a simple root

r

, and let

\{x_n\}

be generated by the secant…

Rewrite the equation

\cos x=x

(radians) as a fixed-point problem

x=g(x)

in three different ways…

Let

f(x)=x^3-7x+6

.

Let I=[a,b] be a closed interval and let

g:I\to

I be continuously differentiable with \max_{x\in I}|g'(x)|\le K<1.

For an

n\times

n dense linear system, Gaussian elimination without pivoting (including the subsequent back…

Consider the

2\times 2

system…

Classify each of the following

3\times

3 matrices as (A) LU-factorizable without pivoting, (B) LU-factorizable…

A three-resistor voltage-divider network is governed by Kirchhoff's laws in the form

Gv=b

, where the conductance…

Let

r=b-A\hat{x}

be the residual of an approximate solution

\hat{x}

to Ax=b, with A\in\mathbb{R}^{n\times n}…

Confirm that the two-sided bound of Problem 69 holds for these numbers (all entries of

A

and

b

are exact…

The Hilbert matrix of order 4 is defined by

H_{ij}=1/(i+j-1)

for i,j=1,2,3,4.