Related papers: Inverse eigenvalues problem of nonnegative matrice…

Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this…

We discuss the eigenvalue problem for 2x2 and 3x3 octonionic Hermitian matrices. In both cases, we give the general solution for real eigenvalues, and we show there are also solutions with non-real eigenvalues.

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…

We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of…

We present a new power method to obtain solutions of eigenvalue problems. The method can determine not only the dominant or lowest eigenvalues but also all eigenvalues without the need for a deflation procedure. The method uses a functional…

The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schr\"odinger equation that couples an…

The worst situation in computing the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation associated with an M-matrix occurs when the corresponding linearizing matrix has two very small eigenvalues, one with positive…

It was recently shown that quantum annealing can be used as an effective, fast subroutine in certain types of matrix factorization algorithms. The quantum annealing algorithm performed best for quick, approximate answers, but performance…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…

We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…

In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is…

We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative…

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…

This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…