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 ...

Discovering faster algorithms for matrix multiplication remains a key pursuit in computer science and numerical linear algebra. Since the pioneering contributions of Strassen and Winograd in the late ...

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 ...

The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...

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 ...

In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the ...

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 ...