Related papers: Inverse eigenvalues problem of nonnegative matrice…
An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…
The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…
In this paper, linearly structured partial polynomial inverse eigenvalue problem is considered for the $n\times n$ matrix polynomial of arbitrary degree $k$. Given a set of $m$ eigenpairs ($1 \leqslant m \leqslant kn$), this problem…
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…
We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…
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…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
In this short note, we present a novel method for computing exact lower and upper bounds of eigenvalues of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and…
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…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
Recently, Malik and Ferreyra introduced the $m$-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of…
The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…
We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…
In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant…