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Proceedings of the American Mathematical Society, 1974 The purpose of this paper is to prove convexity properties for the tensor product, determinant, and permanent of hermitian matrices.
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Computation of Generalized Matrix Functions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2016 We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on Gaussian quadrature and Golub--Kahan bidiagonalization. Block variants are also investigated. Numerical experiments
Arrigo, Francesca +2 more
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Computing matrix functions [PDF]
Acta Numerica, 2010 The need to evaluate a functionf(A)∈ ℂn×nof a matrixA∈ ℂn×narises in a wide and growing number of applications, ranging from the numerical solution of differential equations to measures of the complexity of networks. We give a survey of numerical methods for evaluating matrix functions, along with a brief treatment of the underlying theory and a ...
Higham, Nicholas J., Al-Mohy, Awad H.
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Some relations on Humbert matrix polynomials [PDF]
Mathematica Bohemica, 2016 The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix ...
Ayman Shehata
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An effective recursive formula for the Frobenius covariants in matrix functions
Special Matrices, 2017 For theoretical studies, it is helpful to have an explicit expression for a matrix function. Several methods have been used to determine the required Frobenius covariants.
Schäfer F.
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Explicit formulas for the constituent matrices. Application to the matrix functions
Special Matrices, 2015 We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences.
Taher R. Ben, Rachidi M.
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Bivariate matrix functions [PDF]
Operators and Matrices, 2014 A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing results on linear matrix equations and derivatives of matrix functions.
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Mathematics, 2018 Multiterm fractional differential equations (MTFDEs) nowadays represent a widely used tool to model many important processes, particularly for multirate systems.
Marina Popolizio
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On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation
Mathematics, 2019 Many situations, as for example within the context of Fractional Calculus theory, require computing the Mittag−Leffler (ML) function with matrix arguments. In this paper, we collect theoretical properties of the matrix ML function.
Marina Popolizio
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Some Relations on the rRs(P,Q,z) Matrix Function
Axioms, 2023 In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such ...
Ayman Shehata +2 more
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