Tridiagonal systems of linear equations arise naturally in the numerical treatment of one-dimensional boundary value problems, discretised partial-differential equations and many time-stepping schemes ...

An algorithm is presented for solving a system of linear equations Bu = k where B is tridiagonal and of a special form. This form arises when discretizing the equation - d/dx (p(x) du/dx) = k(x) (with ...

Dozens of machine learning algorithms require computing the inverse of a matrix. Computing a matrix inverse is conceptually easy, but implementation is one of the most difficult tasks in numerical ...

Abstract: The solution of tridiagonal linear systems is used in in various fields and plays a crucial role in numerical simulations. However, there is few efficient solver for tridiagonal linear ...

Matrix classes for matrices that are block-tridiagonal and sparse, and simply "block sparse". These talk together, and furthermore containts an algorithm for inversion of the block-tridiagonal version ...

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with ...

ABSTRACT: Numeric algorithms for solving the linear systems of tridiagonal type have already existed. The well-known Thomas algorithm is an example of such algorithms. The current paper is mainly ...