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We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the…

Classical Analysis and ODEs · Mathematics 2015-05-30 A. Carmona , A. M. Encinas , S. Gago , M. J. Jiménez , M. Mitjana

Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…

The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…

Numerical Analysis · Mathematics 2018-05-08 Iria C. S. Cosme , Isaac F. Fernandes , João L. de Carvalho , Samuel Xavier-de-Souza

The reciprocal Pascal matrix is the Hadamard inverse of the symmetric Pascal matrix. We show that the ordinary matrix inverse of the reciprocal Pascal matrix has integer elements. The proof uses two factorizations of the matrix of super…

Combinatorics · Mathematics 2014-05-27 Thomas M. Richardson

In the current paper the authors linked two methods in order to evaluate general n-th order tridiagonal determinants. A breakdown free numerical algorithm is developed for computing the inverse of any nxn general nonsingular tridiagonal…

Numerical Analysis · Mathematics 2022-08-30 Moawwad El-Mikkawy , Abdelrahman Karawia

A matrix balanced version of the Recursive Centered T Matrix Algorithm (RCTMA) applicable to systems possessing resonant inter-particle couplings is presented. Possible domains of application include systems containing interacting localized…

Optics · Physics 2009-05-21 Brian Stout , Jean-Claude Auger , Alexis Devilez

This paper provides an accurate method to obtain the bidiagonal factorization of many generalized Pascal matrices, which in turn can be used to compute with high relative accuracy the eigenvalues, singular values and inverses of these…

Numerical Analysis · Mathematics 2025-01-22 Jorge Delgado , Héctor Orera , Juan Manuel Peña

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse…

Numerical Analysis · Computer Science 2012-09-11 Hiroyuki Ishigami , Kinji Kimura , Yoshimasa Nakamura

We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of…

Rings and Algebras · Mathematics 2020-03-06 Dorothee Richters , Michael Lass , Andrea Walther , Christian Plessl , Thomas D. Kühne

Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and…

Numerical Analysis · Mathematics 2015-01-05 A. A. Karawia

We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…

Symbolic Computation · Computer Science 2019-03-12 Gennadi Malaschonok , Evgeni Ilchenko

In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…

Symbolic Computation · Computer Science 2024-10-23 Hamid Rahkooy

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices…

Numerical Analysis · Mathematics 2014-10-14 Cheng-yi Zhang , Dan Ye , Cong-lei Zhong , Shuanghua Luo

This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…

Numerical Analysis · Mathematics 2019-03-08 Milena Veneva , Alexander Ayriyan

Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…

Numerical Analysis · Mathematics 2023-11-22 R. Thiru Senthil

This study proposes a recursive and easy-to-implement algorithm to compute the score and Hessian matrix in general regime-switching models. We use simulation to compare the asymptotic variance estimates constructed from the Hessian matrix…

Econometrics · Economics 2026-01-13 Chaojun Li , Shi Qiu

We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix multiplication per iteration loop. This is the record high…

Rings and Algebras · Mathematics 2016-04-28 V. Y. Pan , F. Soleymani , Liang Zhao

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-04 Peter Zaspel

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

Discrete Mathematics · Computer Science 2016-07-04 Hing Leung

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…

Symbolic Computation · Computer Science 2017-02-24 Gennadi Malaschonok