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In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-06-30 Frédéric Hecht , Sidi-Mahmoud Kaber , Lucas Perrin , Alain Plagne , Julien Salomon

This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…

Data Structures and Algorithms · Computer Science 2021-12-01 Erik D. Demaine , Jayson Lynch , Jiaying Sun

We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing…

Combinatorics · Mathematics 2018-10-30 Charles Jordan , Michael Joswig , Lars Kastner

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…

Symbolic Computation · Computer Science 2016-10-06 Moulay A. Barkatou , Maximilian Jaroschek , Suzy S. Maddah

Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…

Computational Geometry · Computer Science 2017-09-01 Dawood Hasanzadeh , Sama Goliaei

A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…

Numerical Analysis · Mathematics 2019-08-30 A. A. Alikhanov , A. M. Apekov , Z. A. Kokov , A. O. Belyaev , L. A. Khamukova

The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much…

Numerical Analysis · Mathematics 2021-06-14 Carlos F. Borges

Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…

Computational Geometry · Computer Science 2024-12-12 Zhengtong Zhu , Zhiyi Chi

Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. As…

Classical Analysis and ODEs · Mathematics 2020-09-25 Hjalmar Rosengren , Michael J. Schlosser

In this case study in ``fully automated enumeration'', we illustrate how to take full advantage of symbolic computation by developing (what we call) `symbolic-dynamical-programming' algorithms for computing many terms of `hard to compute…

Combinatorics · Mathematics 2021-08-26 George Spahn , Doron Zeilberger

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

Numerical Analysis · Mathematics 2026-04-02 Jeffrey Uhlmann

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…

Numerical Analysis · Mathematics 2024-06-11 Dongping Li , Xue Wang , Xiuying Zhang

Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…

Machine Learning · Statistics 2020-03-04 Michael Minyi Zhang , Sinead A. Williamson

The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…

Numerical Analysis · Mathematics 2026-01-21 Holger Boche , Adalbert Fono , Gitta Kutyniok

We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…

Numerical Analysis · Mathematics 2019-05-02 Robert M. Gower , Peter Richtárik

A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The…

Numerical Analysis · Mathematics 2023-12-29 Guillaume Gbikpi-Benissan , Qinmeng Zou , Frédéric Magoulès

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-08-09 Aydın Buluç , John R. Gilbert

This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if a certain Rayleigh quotient matrix is…

Numerical Analysis · Mathematics 2010-01-20 Datian Niu , Xuegang Yuan

A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…

Nuclear Theory · Physics 2015-03-18 F. Q. Luo , M. A. Caprio

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…

Numerical Analysis · Mathematics 2019-02-14 Yiqiu Dong , Per Christian Hansen , Michiel E. Hochstenbach , Nicolai Andre Brogaard Riis