Results 11 to 20 of about 13,801,421 (357)
Axioms, 2023 This paper considers the computation of approximations of matrix functionals of form F(A):=vTf(A)v, where A is a large symmetric positive definite matrix, v is a vector, and f is a Stieltjes function.
Jihan Alahmadi +2 more
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SoftNet: A Package for the Analysis of Complex Networks
Algorithms, 2022 Identifying the most important nodes according to specific centrality indices is an important issue in network analysis. Node metrics based on the computation of functions of the adjacency matrix of a network were defined by Estrada and his collaborators
Caterina Fenu +2 more
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Derivative and higher-order Cauchy integral formula of matrix functions
Open Mathematics, 2021 The derivative of a nn-order matrix function on the complex field is usually defined as a n2{n}^{2}-order matrix, which is not suitable for generalizing Cauchy integral formula of matrix functions to its higher-order derivative form. In this paper, a new
Huang Xiaojie, Liu Zhixiu, Wu Chun
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Marginal Fisher Analysis With Polynomial Matrix Function
IEEE Access, 2022 Marginal fisher analysis (MFA) is a dimensionality reduction method based on a graph embedding framework. In contrast to traditional linear discriminant analysis (LDA), which requires the data to follow a Gaussian distribution, MFA is suitable for non ...
Ruisheng Ran +4 more
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Fractal and Fractional, 2023 The computation of the sign function of a matrix plays a crucial role in various mathematical applications. It provides a matrix-valued mapping that determines the sign of each eigenvalue of a nonsingular matrix.
Lei Shi +4 more
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Efficient Evaluation of Matrix Polynomials beyond the Paterson–Stockmeyer Method
Mathematics, 2021 Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix ...
Jorge Sastre, Javier Ibáñez
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Stability of the Lanczos Method for Matrix Function Approximation [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2017 The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n \times n$ matrix $A$, vector $x$, and function $f$. In exact arithmetic, the method's error after $k$ iterations is bounded by the error of the best degree-$k$ polynomial ...
Cameron Musco +2 more
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Differentiating matrix functions [PDF]
Operators and Matrices, 2013 Multivariable, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We examine the geometry of this space of matrices and conclude that the best notion of differentiation of these matrix-valued functions is differentiation along curves.
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A Note on the Appell Hypergeometric Matrix Function F2
, 2020 In this article, we introduce some of the mathematical properties of the second Appell hypergeometric matrix function F2(A, B1, B2, C1, C2; z, ) including integral representations, transformation formulas, and series formulas.
M. Hidan, M. Abdalla
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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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