Book ChapterDOI
Computing the Inverse Matrix Hyperbolic Sine
João R. Cardoso,F. Silva Leite +1 more
- pp 160-169
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TLDR
In this article, necessary and sufficient conditions for solvability of the matrix equation sinh X = A in the complex and real cases were given and some algorithms for computing one of these solutions were presented.Abstract:
We give necessary and sufficient conditions for solvability of the matrix equation sinh X = A in the complex and real cases and present some algorithms for computing one of these solutions. The numerical features of the algorithms are analysed along with some numerical tests.read more
Citations
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Posted Content
The Link Prediction Problem in Bipartite Networks
TL;DR: In this article, the link prediction problem in bipartite networks was studied and generalized to bipartitite graphs, where the positive-semidefinite kernel constraint was relaxed.
Book ChapterDOI
The link prediction problem in bipartite networks
TL;DR: The link prediction problem in bipartite networks is defined and study, specializing general link prediction algorithms to the bipartites case, leading to several new link prediction pseudokernels such as the matrix hyperbolic sine.
Journal ArticleDOI
The Moser-Veselov equation
João R. Cardoso,F. Silva Leite +1 more
TL;DR: In this article, the authors studied the orthogonal solutions of the matrix equation XJ − JX T = M, where J is symmetric positive definite and M is skew-symmetric.
Journal ArticleDOI
Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms
TL;DR: Theoretical and computational aspects of matrix inverse trigonometric and inverse hyperbolic functions are studied, and the principal values acos, asin, acosh, and asinh are defined and shown to be unique primary matrix functions.
Dissertation
Theory and Algorithms for Periodic Functions of Matrices, with Applications
TL;DR: The matrix unwinding function is shown to be useful for computing the matrix exponential using an idea of argument reduction, and theoretical and computational aspects of matrix inverse trigonometric and inverse hyperbolic functions are studied.
References
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Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Journal ArticleDOI
Computing real square roots of a real matrix
TL;DR: An extension of the Schur method is presented which enables real arithmetic to be used throughout when computing a real square root of a real matrix.
Journal ArticleDOI
Stable iterations for the matrix square root
TL;DR: It is shown that apparently innocuous algorithmic modifications to the Padé iteration can lead to instability, and a perturbation analysis is given to provide some explanation.
Journal ArticleDOI
Condition Estimates for Matrix Functions
Charles Kenney,Alan J. Laub +1 more
TL;DR: In this article, a sensitivity theory based on Frechet derivatives is presented that has both theoretical and computational advantages, and two norm-estimation procedures are given; the first is based on a finite-difference approximation of the Frechet derivative and costs only two extra function evaluations.
Related Papers (5)
Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients
L Jódar,JC Cortés López +1 more