Bibliography on the evaluation of numerical software

Theory of software (68N99) Bibliographies for mathematics in general (00A15) Software, source code, etc. for problems pertaining to numerical analysis (65-04)

Related Items (1)

Progress in computational physics

Uses Software

ITPACK
EISPACK
minpack
Algorithm 524
CADRE
RKF45
PORT
IBESS JBESS
FUNPACK

Cites Work

A Comparison of Some Methods for the Solution of Sparse Overdetermined Systems of Linear Equations
A Portable Extended Precision Arithmetic Package and Library with Fortran Precompiler
Dave—a validation error detection and documentation system for fortran programs
A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations
An Error Functional Expansion for N-Dimensional Quadrature with an Integrand Function Singular at a Point
A Comparison of Several Bandwidth and Profile Reduction Algorithms
On George’s Nested Dissection Method
A Comparison of Three Algorithms for Linear Zero-One Programs
Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers
CDC 6600 Subroutines IBESS and JBESS for Bessel Functions I _υ (x) and J _υ (x), x≥0,υ≥0
The Exact Solution of Linear Equations with Rational Function Coefficients
Multistep Methods Using Higher Derivatives and Damping at Infinity
An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
Solving Nonstiff Ordinary Differential Equations—The State of the Art
Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations
A Crank–Nicolson–$H^{ - 1} $–Galerkin Procedure for Parabolic Problems in a Single-Space Variable
Comparison of Algorithms for Multivariate Rational Approximation
Numerical Experiments Using Dissection Methods to Solve n by n Grid Problems
Bounds and perturbation bounds for the matrix exponential
A comparison of some algorithms for the nonlinear least squares problem
On the Relative Efficiency of Higher Order Collocation Methods for Solving Two-Point Boundary Value Problems
Computational Solution of Linear Two-Point Boundary Value Problems via Orthonormalization
An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
A Comparison of Collocation and Finite Differences for Two-Point Boundary Value Problems
Least Squares Estimation of Discrete Linear Dynamic Systems Using Orthogonal Transformations
A language for inquiring about the run-time behaviour of programs
Algorithms for the regularization of ill-conditioned least squares problems
Evaluation of Repeated Integrals of the Coerror Function
The Computation of Real Fractional Order Bessel Functions of the Second Kind
A technique for comparing automatic quadrature routines
A Comparison of Algorithms for the Exact Solution of Linear Equations
On the structure of zero finders
Difference Methods for Boundary Value Problems with a Singularity of the First Kind
Composite Methods for Hyperbolic Equations
Test data as an aid in proving program correctness
Anomalous Convergence of a Continued Fraction for Ratios of Kummer Functions
Review: Book review
Characterization of Optimal Stepsize Sequences for Methods for Stiff Differential Equations
Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations
Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm
An evaluation of the effectiveness of symbolic testing
The Comparison of Numerical Methods for Solving Polynomial Equations
Fast Poisson Solvers for Problems with Sparsity
Error Estimates for a Stiff Differential Equation Procedure
High accuracy finite difference approximation to solutions of elliptic partial differential equations
Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming
Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
Some Numerical Results Using a Sparse Matrix Updating Formula in Unconstrained Optimization
Sorting on STAR
Theoretical and Empirical Studies of Program Testing
Practical Parallel Band Triangular System Solvers
Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
Comparison of a continuation method with Brent's method for the numerical solution of a single nonlinear equation
On the computational aspects of semi-implicit Runge-Kutta methods
On the Computation of Modified Bessel Function Ratios
A class of first order factorization methods
An Alternative Strategy for Cautions Adaptive Quadrature
Block Implicit One-Step Methods
Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems
Automatic Numerical Quadrature
A Theoretical Criterion for Comparing Runge–Kutta Formulas
The Fourier Method for Nonsmooth Initial Data
A Variable Mesh Finite Difference Method for Solving a Class of Parabolic Differential Equations in One Space Variable
Incomplete Nested Dissection for Solving n by n Grid Problems
An investigation of Romberg quadrature
Nineteen Dubious Ways to Compute the Exponential of a Matrix
Numerical Solutions of a Class of Abel Integral Equations
On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations
Multidimensional Monte Carlo Integration Based on Factorized Approximation Functions
The Extrapolation of First Order Methods for Parabolic Partial Differential Equations. I
Collocation methods for linear elliptic problems
Algorithms for sparse Gaussian elimination with partial pivoting
Blended Linear Multistep Methods
High-level data flow analysis
Algorithms for the Solution of the Nonlinear Least-Squares Problem
The Numerical Solution of Boundary Value Problems for Stiff Differential Equations
An Estimate for the Condition Number of a Matrix
Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error
Die Verfahren vom Brown-Brent-Typ bei gemischt linearen-nichtlinearen Gleichungssystemen
Faster Convergence for Iterative Solutions to Systems via Three-Part Splitting
Stability analysis of certain Runge-Kutta procedures for Volterra integral equations
Ein Abstiegsverfahren für Approximationsaufgaben in normierten Räumen
Extended conjugate-gradient methods with restarts
Moderate-degree tetrahedral quadrature formulas
A Taylor series method for the numerical solution of two-point boundary value problems
Extrapolation methods for dynamic partial differential equations
Review of computing methods for recirculating flows
Fast Poisson solvers on general two dimensional regions for the Dirichlet problem
A performance comparison study between subroutine packages LINSYS, IBMSSP and IMSL for solving systems of linear equations
Optimized block-implicit relaxation
Matrix eigensystem routines - EISPACK guide. 2nd ed
Use of Richardson extrapolation for the numerical calculation of Fourier transforms
A comparison of non-linear equation solvers
Untersuchungen des Zeitgewinns durch neue Algorithmen zur Matrix- Multiplikation
A class of iterative methods for finite element equations
A comparison of numerical methods for the solution of quasilinear equations
A bibliography on automatic integration
Matrix multiplication by diagonals on a vector/parallel processor
Proposal for population studies in numerical quadrature
Automatic computation of integrals with singular integrand, over a finite or an infinite range
Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary value problems
Comparison of some methods for evaluating infinite range oscillatory integrals
On some classes of variationally derived quasi-Newton methods for systems of nonlinear algebraic equations
The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
Matrix eigensystem routines. EISPACK guide extension
Solving a system of linear inequalities for generating test data
High order methods for the numerical integration of ordinary differential equations
Direct solutions for Poisson's equation in three dimensions
Sorting by distributive partitioning
Algorithms for the solution of systems of coupled second-order ordinary differential equations
A factorization method for the solution of constrained linear least squares problems allowing subsequent data changes
Orthogonal collocation on finite elements for elliptic equations
Evaluation of numerical methods for elliptic partial differential equations
The complexity of numerical methods for elliptic partial differential equations
Higher order difference methods for second order two-point boundary-value problems
Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
On the maximal order in PC-codes
Boundary conditions for multistep finite-difference methods for time- dependent equations
On the multi-grid method applied to difference equations
Accurate numerical solutions of boundary layer flows by the finite- difference method of Hermitian type
The operator compact implicit method for parabolic equations
Algorithm 36. SNIFF: Efficient self-tuning algorithm for numerical integration
The nonlinear Volterra equation of Abel's kind and its numerical treatment
On the numerical solution of the eigenvalue problem of the Laplace operator by a capacitance matrix method
Convergence acceleration on a general class of power series
Application of mixed language programming
A projection method for semidefinite linear systems and its applications
New approach to comparison of search methods used in nonlinear programming problems
Numerical Comparisons of Algorithms for Polynomial and Rational Multivariate Approximations
A Comment on: “Numerical Comparisons of Algorithms for Polynomials and Rational Multivariate Approximations”
A User’s View of Solving Stiff Ordinary Differential Equations
A statistical study of the accuracy of floating point number systems
Least Change Secant Updates for Quasi-Newton Methods
Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]
Initial Value Routines in the NAG Library
Stability properties of Adams codes
High-Order Fast Elliptic Equation Solvers
Robust Methods for Solving Systems of Nonlinear Equations
Scattered Data Interpolation: Tests of Some Method
On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels
A User's Guide to the Evaluation of Statistical Packages and Systems
Newton-type methods for unconstrained and linearly constrained optimization
Comparing numerical methods for stiff systems of O.D.E:s
Local Versus Global Strategies for Adaptive Quadrature
A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives
Some Experience with Constructing, Testing, and Certifying a Standard Mathematical Subroutine Library
On Comparing Adams and Natural Spline Multistep Formulas
The FUNPACK Package of Special Function Subroutines
A Comparison of Computational Methods and Algorithms for the Complex Gamma Function
Principles for Testing Polynomial Zerofinding Programs
Software for Nonlinear Partial Differential Equations
The Influence of the Compiler on the Cost of Mathematical Software—in Particular on the Cost of Triangular Factorization
A Unified View of Some Methods for Stiff Two-Point Boundary Value Problems
The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer
Comments on the Nature of Automatic Quadrature Routines
The production of special function routines for a multi-machine library
Fast Multiple-Precision Evaluation of Elementary Functions
Parallel Algorithms for Adaptive Quadrature. III. Program Correctness
Global Error Estimates for Ordinary Differential Equations
An Automatic Program for Linear Fredholm Integral Equations of the Second Kind
Stable Procedures for the Inversion of Abel′s Equation
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Progress in Numerical Analysis
An Automatic Nested Dissection Algorithm for Irregular Finite Element Problems
A Survey of Parallel Algorithms in Numerical Linear Algebra
A stiffly stable integration process using cyclic composite methods
Stability Regions in the Numerical Treatment of Volterra Integral Equations
Algorithm 714: CELEFUNT: a portable test package for complex elementary functions
Eigenvalues of Symmetric Tridiagonal Matrices: A Fast, Accurate and Reliable Algorithm
When Not to Use an Automatic Quadrature Routine
Comparison of some FORTRAN programs for matrix inversion
The Construction of Numerical Subroutine Libraries
The Exact Solution of Systems of Linear Equations with Polynomial Coefficients
A Report on the Accuracy of Some Widely Used Least Squares Computer Programs
The automatic solution of systems of ordinary differential equations by the method of Taylor series
A Doubly-Adaptive Clenshaw-Curtis Quadrature Method
An empirical study of FORTRAN programs
A comparative study of computer programs for integrating differential equations

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