Certified dense linear system solving

Certified Dense Linear System Solving

Certified sparse linear system solving

Solving a large dense linear system by adaptive cross approximation

An efficient algorithm for the direct solution of a linear system associated with the discretization of boundary integral equations with oscillatory kernels (in two dimensions) is described without having to compute the complete matrix of the linear system. This algorithm is based on the unitary-weight representation, for which a new construction based on adaptive cross approximation is propose...

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). ...

CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS). This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrate...