A direct method for the general solution of a system of linear equations

DOI10.1007/BF00933852zbMath0291.90038OpenAlexW2043007775MaRDI QIDQ1211408

S. Singh

Publication date: 1975

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00933852

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Linear programming (90C05) Linear equations (linear algebraic aspects) (15A06)

Related Items

Error analysis of algorithms for computing the projection of a point onto a linear manifold ⋮ Variationally derived algorithms in the ABS class for linear systems ⋮ ON SYSTOLIC GENERAL SYSTEM SOLUTION AND GENERAL MATRIX INVERSION ⋮ Extended reduced rank two Abaffian update schemes in the ABS-type methods ⋮ New interpretation of related Huang's methods ⋮ On systolic general system solution for optimal artificial neural network training ⋮ ABS methods for continuous and integer linear equations and optimization ⋮ Extended rank reduction formulas containing Wedderburn and Abaffy-Broyden-Spedicato rank reducing processes ⋮ On solving sparse band systems with three algorithms of the ABS family ⋮ On the error estimate for the projection of a point onto a linear manifold ⋮ On the numerical stability of Huang's update ⋮ On the ABS algorithm with singular initial matrix and its application to linear programming ⋮ A bibliography of the ABS methods ⋮ Variations on the Gram--Schmidt and the Huang algorithms for linear systems: A numerical study ⋮ A class of quadratically convergent algorithms for constrained function minimization ⋮ Recursive interpolation algorithm: A formalism for solving systems of linear equations. I: Direct methods ⋮ Factorization of matrices over division rings and rings ⋮ Solution of linear least squares via the ABS algorithm ⋮ Optimally conditioned scaled ABS algorithms for linear systems ⋮ A class of scaled direct methods for linear systems ⋮ An optimal linear estimation approach to solve systems of linear algebraic equations ⋮ On the numerical stability of Huang's and related methods ⋮ On the abs algorithms for perturbed linear systems^∗ ⋮ A class of direct methods for linear systems ⋮ ABS algorithms for linear equations and optimization ⋮ Direct methods for the solution of linear systems

Cites Work

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• A Method for Computing the Generalized Inverse of a Matrix
• A computational method for evaluating generalized inverses
• An Elimination Method for Computing the Generalized Inverse of an Arbitrary Complex Matrix
• Unitary Triangularization of a Nonsymmetric Matrix