Inclusion Methods for Multiplication of Three Point Matrices

Abstract

This study considers inclusion methods for the multiplication of three point matrices. These methods are essential for verification methods such as for a matrix determinant, generalized eigenvalue decomposition, singular value decomposition, square roots and inverse square roots of a matrix, and Sylvester equations. We consider three methods that involve five matrix multiplications and compare the tightness of enclosures and numerical experiments. The proposed methods produce tighter results than the previous method with the same computational cost. We also show methods for obtaining the upper bound of the maximum norm of a product of three point matrices.