Solving linear equations over GF(2): Block Lanczos algorithm

DOI10.1016/0024-3795(93)90235-GzbMath0788.65038WikidataQ29543610 ScholiaQ29543610MaRDI QIDQ1311312

Don Coppersmith

Publication date: 30 May 1994

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Gaussian eliminationLanczos algorithmlarge sparse systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (14)

Factoring multivariate polynomials via partial differential equations ⋮ Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations ⋮ A probabilistic approach to problems parameterized above or below tight bounds ⋮ Solving sparse linear systems of equations over finite fields using bit-flipping algorithm ⋮ The universal block Lanczos-Padé method for linear systems over large prime fields ⋮ A Kilobit Special Number Field Sieve Factorization ⋮ \(\mathbb F _2 \) Lanczos revisited ⋮ Subquadratic computation of vector generating polynomials and improvement of the block Wiedemann algorithm ⋮ Simultaneous modular reduction and Kronecker substitution for small finite fields ⋮ Updating key size estimations for pairings ⋮ An Implementation of the Number Field Sieve ⋮ Fast matrix decomposition in \(\mathbb F_2\) ⋮ A Probabilistic Approach to Problems Parameterized above or below Tight Bounds ⋮ Euclid’s algorithm and the Lanczos method over finite fields

Cites Work

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• Discrete logarithms in \(\mathrm{GF}(p)\)
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• Solving sparse linear equations over finite fields
• Solving Homogeneous Linear Equations Over GF(2) via Block Wiedemann Algorithm

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