Jacobi eigenvalue algorithm
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Globally Convergent Jacobi-Type Algorithms for Simultaneous Orthogonal Symmetric Tensor Diagonalization Open
In this paper, we consider a family of Jacobi-type algorithms for\nsimultaneous orthogonal diagonalization problem of symmetric tensors. For the\nJacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013],\nwe prove its g…
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A new generalized Jacobi Galerkin operational matrix of derivatives: two algorithms for solving fourth-order boundary value problems Open
This paper reports a novel Galerkin operational matrix of derivatives of some generalized Jacobi polynomials.This matrix is utilized for solving fourth-order linear and nonlinear boundary value problems.Two algorithms based on applying Gal…
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Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations Open
This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix metho…
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Fast structured Jacobi-Jacobi transforms Open
Jacobi polynomials are frequently used in scientific and engineering applications, and often times, one needs to use the so-called Jacobi-Jacobi transforms which are transforms between two Jacobi expansions with different indices. In this …
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A Shallow Neural Network for Real-Time Embedded Machine Learning for Tensorial Tactile Data Processing Open
This paper presents a novel hardware architecture of the Tensorial Support Vector Machine (TSVM) based on Shallow Neural Networks (NN) for the Single Value Decomposition (SVD) computation. The proposed NN achieves a comparable Mean Squared…
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Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum Open
We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was recently discovered. In this paper, we consider Angelesco systems formed by two analytic weights and obtain a…
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Performance of the parallel block Jacobi method with dynamic ordering for the symmetric eigenvalue problem Open
We investigate the performance of the parallel block Jacobi method for the symmetric eigenvalue problem with dynamic ordering both theoretically and experimentally. First, we present an improved global convergence theorem of the method tha…
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On Optimal Parameter Not Only for the SOR Method Open
The Jacobi, Gauss-Seidel and SOR methods belong to the class of simple iterative methods for linear systems. Because of the parameter , the SOR method is more effective than the Gauss-Seidel method. Here, a new approach to the simple iter…
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The Inverse Spectral Problem for Jacobi-Type Pencils Open
In this paper we study the inverse spectral problem for Jacobi-type pencils. By a Jacobi-type pencil we mean the following pencil J₅−λJ₃, where J₃ is a Jacobi matrix and J₅ is a semi-infinite real symmetric five-diagonal matrix with positi…
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Damped Jacobi Methods Based on Two Different Matrices for Signal Detection in Massive MIMO Uplink Open
For massive multiple-input multiple-output (m-MIMO) uplink, the performances of the linear minimum mean-square error (MMSE) detector are considered near optimal, and they occupy benchmark place for most linear iterative detectors. However,…
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The Characteristic Function for Complex Doubly Infinite Jacobi Matrices Open
We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a…
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Laguerre and Jacobi analogues of the Warren process Open
We define Laguerre and Jacobi analogues of the Warren process. That is, we construct local dynamics on a triangular array of particles so that the projections to each level recover the Laguerre and Jacobi eigenvalue processes of König-O'Co…
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Application of Jacobi and Gauss–Seidel Numerical Iterative Solution Methods for the Stationary Distribution of Markov Chain Open
The Physical or Mathematical behaviour of this model may be represented by describing all the different states it may occupy and by indicating how it moves among these states. In this study, the stationary distribution of Markov chains was…
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Second Refinement of Jacobi Iterative Method for Solving Linear System of Equations Open
In this paper, the new method called second refinement of Jacobi (SRJ) method for solving linear system of equations is proposed. The method can be used to solve ODE and PDE problems where the problems are reduced to linear system of equat…
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Combinatorial preconditioning for accelerating the convergence of the parallel block Jacobi method for the symmetric eigenvalue problem Open
In this paper, we propose combinatorial preconditioning to accelerate the convergence of the parallel block Jacobi method for the symmetric eigenvalue problem. The idea is to gather matrix elements of large modulus near the diagonal prior …
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An Efficient FPGA Implementation of MUSIC Processor Using Cyclic Jacobi Method: LiDAR Applications Open
LiDAR is a technology that uses lasers to measure the position of elements. Measuring the laser travel time and calculating the distance between the LiDAR and the surface requires the calculation of eigenvalues and eigenvectors of the conv…
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Bisymmetric non-negative Jacobi matrix realizations Open
Within the symmetric inverse eigenvalue problem, the case of bisymmetric Jacobi matrices occupies a central place, since for any strictly monotone list of n real numbers there exists a unique bisymmetric Jacobi matrix realizing the list. A…
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SECOND REFINEMENT OF GENERALIZED JACOBI ITERATIVE METHOD FOR SOLVING LINEAR SYSTEM OF EQUATIONS Open
The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. In this paper, we present the new method which is called secondrefinement of generalized Jacobi (SRGJ) method for sol…
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PSOR-Jacobi Algorithm for Accelerated MMSE MIMO Detection Open
This paper proposes the periodical successive over-relaxation (PSOR)-Jacobi algorithm for minimum mean squared error (MMSE) detection of multiple-input multiple-output (MIMO) signals. The proposed algorithm has the advantages of two conven…
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INTERNET OF THINGS-BASED WIRELESS SENSOR NETWORK SYSTEM FOR EARLY DETECTION AND PREVENTION OF VANDALISM/LEAKAGE ON PIPELINE INSTALLATIONS IN THE OIL AND GAS INDUSTRY IN NIGERIA Open
Solving linear systems of equations stands as one of the fundamental challenges in linear algebra, given their prevalence across various fields. The demand for an efficient and rapid method capable of addressing diverse linear systems rema…
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Non-iterative computation of Gauss-Jacobi quadrature by asymptotic expansions for large degree Open
Asymptotic approximations to the zeros of Jacobi polynomials are given, with methods to obtain the coefficients in the expansions. These approximations can be used as standalone methods for the non-iterative computation of the nodes of Gau…
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A Mixed Precision Jacobi SVD Algorithm Open
We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and t…
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A NOTE ON THE JACOBI FIELDS ON MANIFOLDS Open
We consider Jacobi filds as the first derivatives for ${\varepsilon}$, the energy of harmonic extensions, in a given manifold. In this paper we see that the Jacobi fild is bounded by the given boundary map. Here we give no restriction conc…
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An Improved Formula for Jacobi Rotations Open
We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real symmetric 2x2 matrix.
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Non-iterative computation of Gauss-Jacobi quadrature Open
Asymptotic approximations to the zeros of Jacobi polynomials are given, with methods to obtain the coefficients in the expansions. These approximations can be used as standalone methods for the non-iterative computation of the nodes of Gau…
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A mixed precision Jacobi SVD algorithm Open
We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and …
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Matrix Algorithms Based on Jacobi and Romanovski-Jacobi Polynomials for Solving the FitzHugh-Nagumo Nonlinear Equation Open
The present paper develops and makes efficient, a new, state-of-theart numerical technique for solving the FitzHugh-Nagumo Nonlinear Equation (FH-NNE) with initial and boundary conditions, which represents perhaps the simplest mathematical…
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An iterative Jacobi-like algorithm to compute a few sparse eigenvalue-eigenvector pairs. Open
In this paper, we describe a new algorithm to compute the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi transformation method for symmetric matrix diagonaliza…
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On a pre-Jacobi-Jordan algebra: relevant properties and double construction Open
We introduce a pre-Jacobi-Jordan algebras and study some relevant properties such as bimodules, matched pairs. Besides, we established a pre-Jacobi-Jordan algebra built as a direct sum of a given pre-Jacobi-Jordan algebra $(\A, \cdot)$ and…
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An iterative Jacobi-like algorithm to compute a few sparse approximate eigenvectors Open
In this paper, we describe a new algorithm that approximates the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi eigenvalue method for symmetric matrices diagon…