NUM:010217A bisection count is a width certificate, not a residual testView access optionsNum Bisection Width CertificateNum Ivt Uniqueness EnclosureRoot finding and nonlinear systemsNumerical Methods · Mixed review—
NUM:010218Secant through two values is superlinear and is not Newton's tangentView access optionsNum Secant Interpolant UpdateNum Secant Order Versus NewtonRoot finding and nonlinear systemsNumerical Methods · Mixed review—
NUM:010219A fixed-point rearrangement is useless unless it contracts on an invariant intervalView access optionsNum Contraction Mapping Invariant IntervalNum Picard Apriori BoundRoot finding and nonlinear systemsNumerical Methods · Mixed review—
NUM:010324Two conjugate-gradient steps close an SPD two-by-two residualView access optionsNum CG Exact IterationNum CG A Orthogonality Finite TerminationLinear systems, least squares, and eigenproblemsNumerical Methods · Mixed review—
NUM:010325Two Householder reflectors expose a least-squares residualView access optionsNum Householder Reflector QRNum QR Least Squares Residual ProjectionLinear systems, least squares, and eigenproblemsNumerical Methods · Mixed review—
NUM:010326An isolated Gershgorin disk names the target of power iterationView access optionsNum Gershgorin IsolationNum Power Iteration Rayleigh QuotientLinear systems, least squares, and eigenproblemsNumerical Methods · Mixed review—
NUM:010420Matching values and derivatives needs repeated-node divided differencesView access optionsNum Hermite Repeated Node Divided DifferencesNum Hermite Remainder IdentityInterpolation and approximationNumerical Methods · Mixed review—
NUM:010421Natural end conditions make a cubic spline, not the interpolating quadraticView access optionsNum Natural Cubic Moment SystemNum Spline Evaluation Versus PolynomialInterpolation and approximationNumerical Methods · Mixed review—
NUM:010522Two Gauss nodes integrate cubics exactly and miss a concrete quarticView access optionsNum Gauss Legendre Nodes WeightsNum Gauss Legendre Degree Error AuditNumerical differentiation and quadratureNumerical Methods · Mixed review—
NUM:010523A trapezoid Romberg triangle recovers the integral of a fifth powerView access optionsNum Romberg Trapezoid TableNum Richardson Even Powers ExactnessNumerical differentiation and quadratureNumerical Methods · Mixed review—
NUM:010531A Monte Carlo mean is unbiased, but Chebyshev still buys the sample sizeView access optionsNum Monte Carlo Unbiased VarianceNum Chebyshev Sample Size CertificateNumerical differentiation and quadratureNumerical Methods · Mixed review—
NUM:010627One classical RK4 step is fifth-order locally and fourth-order globallyView access optionsNum Rk4 Stage ArithmeticNum Onestep Local Versus Global OrderNumerical ODE and introductory PDE methodsNumerical Methods · Mixed review—
NUM:010628An AB2 predictor needs a second value before the AM2 corrector can startView access optionsNum Adams Interpolant DerivationNum Pece Starting Value AuditNumerical ODE and introductory PDE methodsNumerical Methods · Mixed review—
NUM:010629Linear shooting hits the far boundary in one sensitivity stepView access optionsNum Linear Shooting Two IvpNum Sensitivity Newton For Missing SlopeNumerical ODE and introductory PDE methodsNumerical Methods · Mixed review—
NUM:010630A two-node Poisson grid makes truncation visible and quadratics exactView access optionsNum Centered Difference TruncationNum Small Grid Poisson SolveNumerical ODE and introductory PDE methodsNumerical Methods · Mixed review—
NUM:9922001A decimal floating-point system uses base \beta = 10, precision t = 4, and exponent range -2 \le e \le 3.View problem statementError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922002In IEEE-style binary floating-point with base \beta = 2, precision t, and rounding to nearest (ties to even), the u…View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
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…View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922004Let \varepsilon_{\mathrm{mach}} be the machine epsilon of a rounding-to-nearest binary floating-point system.View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922005Suppose all elementary operations are performed in floating-point arithmetic satisfying \mathrm{fl}(a \odot b) = (a…View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922006Let f(x) = \sqrt{1+x}-1 for x > -1.View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922007The quadratic equation ax^2 + bx + c = 0 with a \ne 0 has roots when b^2-4ac \ge 0.View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922008Define the absolute condition number of a differentiable scalar function f at x by \kappa_{\mathrm{abs}}(x) = |f'(x…View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—
NUM:9922009Consider evaluating p(x) = x^2 - 2x + 1 at machine numbers near x = 1.View access optionsError ConditioningNumerical Methods Problem SolvingFloating-point arithmetic, conditioning, and stabilityNumerical Methods · Calculation—