Premium
Complex Falk‐Langemeyer Method
Author(s) -
Hari Vjeran
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800020
Subject(s) - positive definite matrix , hermitian matrix , block matrix , mathematics , stability (learning theory) , matrix (chemical analysis) , block (permutation group theory) , algebra over a field , combinatorics , computer science , pure mathematics , physics , eigenvalues and eigenvectors , materials science , quantum mechanics , composite material , machine learning
The known Falk‐Langemeyer method for the simultaneous diagonalization of two positive definite symmetric matrices is generalized to work with complex matrices. It is shown that the derived method is well defined for the Hermitian matrices which make a definite pair. Special attention is paid to the stability of the formulas for the computational parameters when the pivot submatrices are close to being proportional. Numerical tests indicate the high relative accuracy of the method provided that both matrices are definite and well‐behaved, i.e. if they can be well‐scaled symmetrically.