scientific article; zbMATH DE number 7280141

zbMath1448.65023MaRDI QIDQ5137445

Abdellah Salhi, Muhammad Farooq

Publication date: 2 December 2020

Full work available at URL: http://jprm.sms.edu.pk/a-new-lanczos-type-algorithm-for-systems-of-linear-equations/

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

formal orthogonal polynomialsLanczos algorithmArnoldi algorithmsystems of linear equations

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Uses Software

• na1

Cites Work

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• Padé-type approximation and general orthogonal polynomials
• A breakdown-free Lanczos type algorithm for solving linear systems
• An iterative solution method for solving \(f(A)x=b\), using Krylov subspace information obtained for the symmetric positive definite matrix A
• A new linear programming algorithm - better or worse than the simplex method?
• A new presentation of orthogonal polynomials with applications to their computation
• Avoiding breakdown and near-breakdown in Lanczos type algorithms
• Hybrid procedures for solving linear systems
• The matrix and polynomial approaches to Lanczos-type algorithms
• A review of formal orthogonality in Lanczos-based methods
• Lanczos-type algorithms for solving systems of linear equations
• New look-ahead Lanczos-type algorithms for linear systems
• New implementations of Lanczos method
• A regularizing Lanczos iteration method for underdetermined linear systems
• Krylov solvers for linear algebraic systems.
• IMPROVING THE SOLVABILITY OF ILL-CONDITIONED SYSTEMS OF LINEAR EQUATIONS BY REDUCING THE CONDITION NUMBER OF THEIR MATRICES
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• The Lanczos Algorithm with Selective Orthogonalization
• Stability of Conjugate Gradient and Lanczos Methods for Linear Least Squares Problems
• A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms
• On the Lanczos Method for Solving Symmetric Linear Systems with Several Right-Hand Sides
• New Recurrence Relationships between Orthogonal Polynomials which Lead to New Lanczos-type Algorithms
• The Lanczos and Conjugate Gradient Algorithms
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems