New methods for evaluating the validity of the results of mathematical computations

DOI10.1016/0378-4754(78)90016-2zbMath0437.65041OpenAlexW2089961863MaRDI QIDQ1141462

Publication date: 1978

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4754(78)90016-2

zbMATH Keywords

Fast Fourier Transform permutation-perturbation method elementary functionals exact number of significant decimal digits precision of computed results

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Roundoff error (65G50) Algorithms for approximation of functions (65D15) Numerical methods for trigonometric approximation and interpolation (65T40) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

A reliable algorithm to check the accuracy of iterative schemes for solving nonlinear equations: an application of the CESTAC method ⋮ The equality relations in scientific computing ⋮ Stochastic approach of the permutation-perturbation method for round-off error analysis ⋮ Computing roots of polynomials on vector processing machines ⋮ Breakdown and near-breakdown control in the CGS algorithm using stochastic arithmetic ⋮ Review on stochastic approach to round-off error analysis and its applications ⋮ Floating-point error propagation in iterative methods ⋮ Sturm sequences and the number of zeros of a real polynomial in the unit disk: Numerical computation ⋮ All possible computed results in correct floating-point summation ⋮ Numerical accuracy control in fixed-point arithmetic ⋮ Data error analysis in unconstrained optimization problems with the CESTAC method ⋮ A variant of the CESTAC method and its application to constrained optimization ⋮ Practical methods for evaluating the accuracy of the eigenelements of a symmetric matrix ⋮ Validation of results of collocation methods for ODEs with CADNA library ⋮ A software for evaluating local accuracy in the Fourier transform ⋮ A novel numerical optimality technique to find the optimal results of Volterra integral equation of the second kind with discontinuous kernel ⋮ Finding an optimal partition for a numerical integration using the trapezoidal rule ⋮ Détermination d'un pas optimum d'intégration pour la méthode de Simpson ⋮ Numerical estimation of the first order derivative: Approximate evaluation of an optimal step ⋮ Applied computational geometry: Towards robust solutions of basic problems ⋮ Linear and non-linear programming software validity ⋮ Stabilizing Bairstow's method ⋮ The use of the CADNA library for validating the numerical results of the hybrid GMRES algorithm ⋮ A procedure with stepsize control for solving \(n\) one-dimensional IVPs ⋮ Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic ⋮ Experiments on the evaluation of functional ranges using a random interval arithmetic ⋮ Numerical accuracy of a certain class of iterative methods for solving linear system ⋮ Stepsize control for cubic spline interpolation ⋮ A Schur's modified sequence and the number of zeros of a real polynomial in the unit disk: Testing its numerical quality ⋮ Optimal iterate of the power and inverse iteration methods ⋮ Comparison of four software packages applied to a scattering problem ⋮ Stochastic Rounding and Its Probabilistic Backward Error Analysis ⋮ An efficient implementation of optimization algorithms

Cites Work