Certified sparse linear system solving

Certified sparse linear system solving

Certified Dense Linear System Solving

Solving Sparse Linear Constraints

Linear arithmetic decision procedures form an important part of theorem provers for program verification. In most verification benchmarks, the linear arithmetic constraints are dominated by simple difference constraints of the form x ≤ y + c. Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints. In this paper, we propose an eff...

Solving Sparse Integer Linear Systems

We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a p-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic complexity in terms of machine operations subject to a conjecture on the e ectiveness of certain sparse projections. A LinBox based implementation of this algorithm ...

Certified Diophantine Solving of Linear Systems in LinBox

LinBox[6] is a C++ template library for high-performance exact linear algebra. It provides optimized facilities for solving rational systems, and computing invariants and canonical forms of linear operators. It acts as middleware on top of existing low-level software libraries for multiprecision integer arithmetic (GMP, NTL), finite field algebra (Givaro, NTL) and linear algebra (BLAS, ATLAS). ...