Complex Falk‐Langemeyer Method

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...

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Bibliographic Details
Published in:Proceedings in applied mathematics and mechanics 2018-12, Vol.18 (1), p.n/a
Main Author: Hari, Vjeran
Format: Article
Language:English
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Summary: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.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.201800020