Matrix polynomials with partially prescribed eigenstructure: eigenvalue sensitivity and condition estimation
نویسندگان
چکیده
منابع مشابه
Matrix Polynomials with Completely Prescribed Eigenstructure
We present necessary and sufficient conditions for the existence of a matrix polynomial when its degree, its finite and infinite elementary divisors, and its left and right minimal indices are prescribed. These conditions hold for arbitrary infinite fields and are determined mainly by the “index sum theorem”, which is a fundamental relationship between the rank, the degree, the sum of all parti...
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For a matrix polynomial P (λ) and a given complex number μ, we introduce a (spectral norm) distance from P (λ) to the matrix polynomials that have μ as an eigenvalue of geometric multiplicity at least κ, and a distance from P (λ) to the matrix polynomials that have μ as a multiple eigenvalue. Then we compute the first distance and obtain bounds for the second one, constructing associated pertur...
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Consider an n × <span style="fon...
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ژورنال
عنوان ژورنال: Computational & Applied Mathematics
سال: 2005
ISSN: 0101-8205
DOI: 10.1590/s0101-82052005000300003