Certified dense linear system solving

DOI10.1016/j.jsc.2003.07.004zbMath1137.11361OpenAlexW2079533520MaRDI QIDQ2643521

Arne Storjohann, Thom Mulders

Publication date: 24 August 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/68735

zbMATH Keywords

randomized algorithminteger matrixpolynomial matrixLas VegasDiophantine system solutionlinear system solution

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (18)

High-order lifting and integrality certification ⋮ The shifted number system for fast linear algebra on integer matrices ⋮ Certified dense linear system solving ⋮ Certified sparse linear system solving ⋮ Triangular \(x\)-basis decompositions and derandomization of linear algebra algorithms over \(K[x\)] ⋮ On lattice reduction for polynomial matrices ⋮ On the complexity of inverting integer and polynomial matrices ⋮ On computation of the greatest common divisor of several polynomials over a finite field. ⋮ Geometrical regular languages and linear Diophantine equations: the strongly connected case ⋮ Computing the sign or the value of the determinant of an integer matrix, a complexity survey. ⋮ Package of procedures for inverting matrices whose entries are linear difference operators ⋮ Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization ⋮ Verification protocols with sub-linear communication for polynomial matrix operations ⋮ On the solvability of a system of linear equations over the domain of principal ideals ⋮ Geometrical Regular Languages and Linear Diophantine Equations ⋮ A \(p\)-adic algorithm for computing the inverse of integer matrices ⋮ Computing the Mazur and Swinnerton-Dyer critical subgroup of elliptic curves ⋮ On the Differential and Full Algebraic Complexities of Operator Matrices Transformations

Cites Work

• Exact solution of linear equations using p-adic expansions
• High-order lifting and integrality certification
• Approximate formulas for some functions of prime numbers
• Certified dense linear system solving
• Rational solutions of singular linear systems
• Matrix Analysis
• Solving sparse linear equations over finite fields
• Acceleration of Euclidean Algorithm and Rational Number Reconstruction
• Nearly Optimal Algorithms for Canonical Matrix Forms
• Fast construction of irreducible polynomials over finite fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Certified dense linear system solving