Results 21 to 30 of about 1,484,501 (262)
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 ...
Nicholas J. Higham, Awad H. Al-Mohy
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Computational Graphs for Matrix Functions
ACM Transactions on Mathematical Software, 2022 Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve them, and eventually derive new ones.
Elias Jarlebring +2 more
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Stochastic Conditioning of Matrix Functions [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2014 We investigate the sensitivity of matrix functions to random noise in their input. We propose the notion of a stochastic condition number, which determines, to first order, the sensitivity of a matrix function to random noise. We derive an upper bound on the stochastic condition number that can be estimated efficiently by using “small-sample ...
Gratton, Serge, Titley-Peloquin, David
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Algorithms, 2020 We propose and investigate two new methods to approximate f(A)b for large, sparse, Hermitian matrices A. Computations of this form play an important role in numerous signal processing and machine learning tasks.
Tiffany Fan +3 more
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Variational Properties of Matrix Functions via the Generalized Matrix-Fractional Function [PDF]
SIAM Journal on Optimization, 2019 We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which such functions are closed and proper as well as formulas for the ready computation of both their conjugates and ...
James V. Burke, Yuan Gao, Tim Hoheisel
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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
Francesca Arrigo +2 more
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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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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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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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