Accurate Computations with Block Checkerboard Pattern Matrices

Abstract

In this work, block checkerboard sign pattern matrices are introduced and analyzed. They satisfy the generalized Perron–Frobenius theorem. We study the case related to total positive matrices in order to guarantee bidiagonal decompositions and some linear algebra computations with high relative accuracy. A result on intervals of checkerboard matrices is included. Some numerical examples illustrate the theoretical results.

Keywords

• bidiagonal decomposition
• high relative accuracy
• total positivity
• block checkerboard pattern