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Computing the Zeros of Quaternion Polynomials
Abstract A method is developed to compute the zeros of a quaternion polynomial with all terms of the form q k X k . This method is based essentially in Niven's algorithm [1], which consists ofExpand
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On solvents of matrix polynomials
First, the basic theory of matrix polynomials and the construction of solvents are reviewed in terms of the concept of eigenpair. Then a study of the number of solvents is done. Conditions for theExpand
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A fixed point method to compute solvents of matrix polynomials
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricialExpand
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Deflation for block eigenvalues of block partitioned matrices with an application to matrix polynomials of commuting matrices
Abstract A method for computing a complete set of block eigenvalues for a block partitioned matrix using a generalized form of Wielandt's deflation is presented. An application of this process isExpand
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Minimal Rank Completions of Partial Matrices
The cyclic rank completion problem with general blocks
We present an upper bound for the minimal completion rank of a partial matrix P whose block pattern is a single cycle of size with specified blocks . Under certain conditions, the bound becomes quiteExpand
Matrix polynomials: Factorization via bisolvents
Abstract We reconsider the classification of all the factorizations of a matrix polynomial P as P = Q R with Q a matrix polynomial and R ( λ ) = λ T − S a regular matrix pencil. It is shown that theExpand
Stability of Matrix Differential Equations with Commuting Matrix Constant Coefficients
Sufficient conditions for the asymptotic stability of systems of first order linear differential equations with commuting matrix constant coefficients is studied. Stability criterion in terms ofExpand
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The cyclic rank completion problem with regular blocks
Abstract A tight upper bound is obtained for the minimal completion rank of a partial block matrix P whose block pattern is a single bipartite cycle of order 2k and with specified blocks of order nExpand
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