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

Num Bisection Width CertificateNum Ivt Uniqueness Enclosure

Root finding and nonlinear systemsNumerical Methods · Mixed review

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

Num Secant Interpolant UpdateNum Secant Order Versus Newton

Root finding and nonlinear systemsNumerical Methods · Mixed review

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

Num Contraction Mapping Invariant IntervalNum Picard Apriori Bound

Root finding and nonlinear systemsNumerical Methods · Mixed review

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

Num CG Exact IterationNum CG A Orthogonality Finite Termination

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

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

Num Householder Reflector QRNum QR Least Squares Residual Projection

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

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

Num Gershgorin IsolationNum Power Iteration Rayleigh Quotient

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

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

Num Hermite Repeated Node Divided DifferencesNum Hermite Remainder Identity

Interpolation and approximationNumerical Methods · Mixed review

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

Num Natural Cubic Moment SystemNum Spline Evaluation Versus Polynomial

Interpolation and approximationNumerical Methods · Mixed review

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

Num Gauss Legendre Nodes WeightsNum Gauss Legendre Degree Error Audit

Numerical differentiation and quadratureNumerical Methods · Mixed review

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

Num Romberg Trapezoid TableNum Richardson Even Powers Exactness

Numerical differentiation and quadratureNumerical Methods · Mixed review

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

Num Monte Carlo Unbiased VarianceNum Chebyshev Sample Size Certificate

Numerical differentiation and quadratureNumerical Methods · Mixed review

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

Num Rk4 Stage ArithmeticNum Onestep Local Versus Global Order

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

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

Num Adams Interpolant DerivationNum Pece Starting Value Audit

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review

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

Num Linear Shooting Two IvpNum Sensitivity Newton For Missing Slope

Numerical ODE and introductory PDE methodsNumerical Methods · Mixed review