Efficient matrix preconditioners for black box linear algebra

Efficient matrix preconditioners for black box linear algebra

The main idea of the “black box” approach in exact linear algebra is to reduce matrix problems to the computation of minimum polynomials. In most cases preconditioning is necessary to obtain the desired result. Here good preconditioners will be used to ensure geometrical/algebraic properties on matrices, rather than numerical ones, so we do not address a condition number. We offer a review of p...

Black Box Linear Algebra with the LinBox Library

Base Class Field Archetype virtual functions pointers

Some results on Haar wavelets matrix through linear algebra

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

Linear Algebra and Matrix Theory

Asynchronous Preconditioners for Efficient Solving of Non-linear Deformations

In this paper, we present a set of methods to improve numerical solvers, as used in real-time non-linear deformable models based on implicit integration schemes. The proposed approach is particularly beneficial to simulate nonhomogeneous objects or ill-conditioned problem at high frequency. The first contribution is to desynchronize the computation of a preconditioner from the simulation loop. ...