An efficient and stable Newton-type iterative method for computing generalized inverse \(A_{T,S}^{(2)}\)

DOI10.1007/s11075-014-9913-1zbMath1335.65043OpenAlexW1980477935MaRDI QIDQ2356070

Fazlollah Soleymani

Publication date: 28 July 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-014-9913-1

zbMATH Keywords

convergencenumerical exampleerror boundToeplitz matrixiterative methodsHankel matrixgeneralized inverseouter inverseefficiency indexlarge sparse matriceshyperpower iterationmatrix-matrix multiplicationprogramming package Mathematica 8Schulz scheme

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Iterative numerical methods for linear systems (65F10) Complexity and performance of numerical algorithms (65Y20)

Related Items (9)

A globally convergent variant of mid-point method for finding the matrix sign ⋮ A quartically convergent Jarratt-type method for nonlinear system of equations ⋮ Some matrix iterations for computing generalized inverses and balancing chemical equations ⋮ On hyperpower family of iterations for computing outer inverses possessing high efficiencies ⋮ Higher-order derivative-free families of Chebyshev-Halley type methods with or without memory for solving nonlinear equations ⋮ An efficient computation of generalized inverse of a matrix ⋮ Approximate Schur-block ILU preconditioners for regularized solution of discrete ill-posed problems ⋮ A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis ⋮ Hyperpower least squares progressive iterative approximation

Uses Software

• Mathematica
• mftoolbox

Cites Work

• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method
• Generalized inverses. Theory and applications.
• A family of iterative methods for computing Moore-Penrose inverse of a matrix
• A class of numerical algorithms for computing outer inverses
• Superfast solution of linear convolutional Volterra equations using QTT approximation
• Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices
• An iterative algorithm to compute the Bott-Duffin inverse and generalized Bott-Duffin inverse
• An Improved Newton Iteration for the Generalized Inverse of a Matrix, with Applications
• Anwendung des Schulz‐Verfahrens zur Nachkorrektur einer näherungsweise berechneten verallgemeinerten Inversen einer Matrix
• Inverse Order Rule for Weighted Generalized Inverse
• Optimal Order of One-Point and Multipoint Iteration
• Functions of Matrices
• The Mathematica GuideBook for Numerics

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