Related papers: Efficient method for calculating the eigenvalue of…
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor…
A numerical method to solve the direct scattering problem for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schroedinger equation is proposed. The method involves the numerical solution of Volterra…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
Given the $n\times n$ matrix polynomial $P(x)=\sum_{i=0}^kP_i x^i$, we consider the associated polynomial eigenvalue problem. This problem, viewed in terms of computing the roots of the scalar polynomial $\det P(x)$, is treated in…
We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and…
Bohr-Sommerfeld type quantization conditions of semiclassical eigenvalues for the non-selfadjoint Zakharov-Shabat operator on the circle are derived using an exact WKB method. The conditions are given in terms of the action associated with…
We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The…
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The…
We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…