Eigenvalue bounds for matrix polynomials in generalized bases
نویسندگان
چکیده
منابع مشابه
Generalized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
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Upper and lower bounds are derived for the absolute values of the eigenvalues of a matrix polynomial (or λ-matrix). The bounds are based on norms of the coefficient matrices and involve the inverses of the leading and trailing coefficient matrices. They generalize various existing bounds for scalar polynomials and single matrices. A variety of tools are used in the derivations, including block ...
متن کاملgeneralized numerical ranges of matrix polynomials
in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.
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A procedure is presented for the computation of bounds to eigenvalues of the generalized hermitian eigenvalue problem and to the standard hermitian eigenvalue problem. This procedure is applicable to iterative subspace eigenvalue methods and to both outer and inner eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the proc...
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Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2017
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3252