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A matrix constructive method for the analytic-numerical solution of coupled partial differential systems

Lucas Jódar, Enrique A. Navarro, M. V. Ferrer (1995)

Applications of Mathematics

In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation u t - A u x x - B u = 0 , where B is an arbitrary square complex matrix and A ia s matrix such that the real part of the eigenvalues of the matrix 1 2 ( A + A H ) is positive. Given an admissible error ε and a finite domain G , and analytic-numerical solution whose error is uniformly upper bounded by ε in G , is constructed.

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin (2016)

Czechoslovak Mathematical Journal

Fiedler and Markham (1994) proved det H ^ k k det H , where H = ( H i j ) i , j = 1 n is a positive semidefinite matrix partitioned into n × n blocks with each block k × k and H ^ = ( tr H i j ) i , j = 1 n . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove det ( I n + H ^ ) det ( I n k + k H ) 1 / k .

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