Test procedures and test problems for least squares algorithms

DOI10.1016/0304-4076(80)90049-4zbMath0421.65041OpenAlexW2028315497MaRDI QIDQ1133296

Roy H. Wampler

Publication date: 1980

Published in: Journal of Econometrics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4076(80)90049-4

zbMATH Keywords

numerical examplessingular value decompositionGram-Schmidt orthogonalizationleast squares algorithmsCholesky decompositionHouseholder transformationprogramsconditioning of matricesCivens transformationclassification of test problemsscaling of the data

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Quadratic programming (90C20) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Orthogonalization in numerical linear algebra (65F25) Software, source code, etc. for problems pertaining to numerical analysis (65-04)

Related Items

Centering and scaling of regression algorithms in the face of iii–conditioning, Benchmarking numerical accuracy of statistical algorithms

Uses Software

• AS 79
• AS 75

Cites Work

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• A direct error analysis for least squares
• Numerical methods for solving linear least squares problems
• Handbook series linear algebra. Linear least squares solutions by Householder transformations
• Elimination with weighted row combinations for solving linear equations and least squares problems
• Note on the iterative refinement of least squares solution
• Singular value decomposition and least squares solutions
• Jordan-Elimination und Ausgleichung nach kleinsten Quadraten
• SWAC Experiments on the Use of Orthogonal Polynomials for Data Fitting
• Numerical Methods in Scientific Computing, Volume I
• Solutions to Weighted Least Squares Problems by Modified Gram-Schmidt with Iterative Refinement
• Discrete least squares polynomial fits
• Computing methods for linear models subject to linear parametric constraints
• On the Iterative Refinement of Least Squares Solutions
• The Acceptability of Regression Solutions: Another Look at Computational Accuracy
• A test of the numerical accuracy of some matrix inversion algorithms commonly used in least squares programs
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• Least squares computations based on the cholesky decomposition of the correlation matrix
• Tolerance and Condition in Regression Computations
• Numerical Methods for Computing Angles Between Linear Subspaces
• Linear Least Squares by Elimination and MGS
• A Note on Implementing the Householder Transformation
• Experiments on Error Growth Associated with Some Linear Least-Squares Procedures
• Iterative refinement of linear least squares solutions II
• An evaluation of linear least squares computer programs
• Solving equations exactly
• Solving linear least squares problems by Gram-Schmidt orthogonalization
• The least squares problem and pseudo-inverses
• A Report on the Accuracy of Some Widely Used Least Squares Computer Programs
• On the Numerical Solution of Constrained Least-Squares Problems
• A New Method for Examining Rounding Error in Least-Squares Regression Computer Programs
• Round off error analysis for Gram-Schmidt method and solution of linear least squares problems
• Test Data for Statistical Algorithms: Least Squares and ANOVA