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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…

Numerical Analysis · Mathematics 2025-09-16 Cristian Rusu

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…

Numerical Analysis · Mathematics 2013-11-20 Giorgio Mantica

This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during…

We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The…

Numerical Analysis · Mathematics 2026-05-27 Simon Mataigne , P. -A. Absil

In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…

Optimization and Control · Mathematics 2008-09-23 Dang Doan , Tamas Keviczky , Ion Necoara , Moritz Diehl

A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are characterized. Such families are very general,…

Mathematical Physics · Physics 2019-11-05 Benito Hernández-Bermejo

In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix…

We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that…

Differential Geometry · Mathematics 2023-09-01 Katarina Lukić

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…

Chemical Physics · Physics 2009-11-06 N. Mosyagin , E. Eliav , U. Kaldor

We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the classical symmetric weight function for the Jacobi…

Classical Analysis and ODEs · Mathematics 2007-05-23 J. Koekoek , R. Koekoek

The Eberlein method is a Jacobi-type process for solving the eigenvalue problem of an arbitrary matrix. In each iteration two transformations are applied on the underlying matrix, a plane rotation and a non-unitary elementary…

Numerical Analysis · Mathematics 2024-07-12 Erna Begovic , Ana Perkovic

Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…

Classical Analysis and ODEs · Mathematics 2009-09-25 André Ronveaux , Walter Van Assche

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

Numerical Analysis · Mathematics 2013-12-31 Na Li , Carmeliza Navasca

This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\ 140 (2013), 248--292] where mapping properties of several fundamental harmonic analysis operators in the setting of symmetrized Jacobi trigonometric expansions were…

Classical Analysis and ODEs · Mathematics 2015-12-31 Bartosz Langowski

We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to the classical weight function for the Jacobi polynomials together with point masses at both…

Classical Analysis and ODEs · Mathematics 2007-05-23 Roelof Koekoek

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…

Numerical Analysis · Computer Science 2020-03-18 Sanja Singer , Sasa Singer , Vedran Novakovic , Davor Davidovic , Kresimir Bokulic , Aleksandar Uscumlic

This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…

Numerical Analysis · Mathematics 2018-04-30 Geoff Vasil , Daniel Lecoanet , Keaton Burns , Jeff Oishi , Ben Brown

We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…

Optimization and Control · Mathematics 2021-02-10 Miguel D. Bustamante , Pauline Mellon , M. Victoria Velasco

We show that $\lambda$-symmetries can be algorithmically obtained by using the Jacobi last multiplier. Several examples are provided.

Mathematical Physics · Physics 2011-11-08 M. C. Nucci , D. Levi

A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for…

Mathematical Physics · Physics 2016-10-28 Hermann Schulz-Baldes