Palindromic companion forms for matrix polynomials of odd degree
نویسندگان
چکیده
منابع مشابه
Palindromic companion forms for matrix polynomials of odd degree
The standard way to solve polynomial eigenvalue problems P (λ)x = 0 is to convert the matrix polynomial P (λ) into a matrix pencil that preserves its spectral information– a process known as linearization. When P (λ) is palindromic, the eigenvalues, elementary divisors, and minimal indices of P (λ) have certain symmetries that can be lost when using the classical first and second Frobenius comp...
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Many applications give rise to matrix polynomials whose coefficients have a kind of reversal symmetry, a structure we call palindromic. Several properties of scalar palindromic polynomials are derived, and together with properties of compound matrices, used to establish the Smith form of regular and singular T -palindromic matrix polynomials over arbitrary fields. The invariant polynomials are ...
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In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...
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Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...
متن کاملEla Palindromic Linearizations of a Matrix Polynomial of Odd Degree Obtained from Fiedler Pencils with Repetition
Many applications give rise to structured, in particular T-palindromic, matrix polynomials. In order to solve a polynomial eigenvalue problem P (λ)x = 0, where P (λ) is a T-palindromic matrix polynomial, it is convenient to use palindromic linearizations to ensure that the symmetries in the eigenvalues, elementary divisors, and minimal indices of P (λ) due to the palindromicity are preserved. I...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2011
ISSN: 0377-0427
DOI: 10.1016/j.cam.2011.09.010