Related papers: A Mixed Precision Eigensolver Based on the Jacobi …
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…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…
We analyze several versions of Jacobi's method for the symmetric eigenvalue problem. Our goal is to reduce the asymptotic cost of the algorithm as much as possible, as measured by the number of arithmetic operations performed and associated…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity. Given an isolated singular zero of a square analytic…
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…
We consider the solution of the Sylvester equation $AX+XB=C$ in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations; our rounding error analysis provides sufficient conditions…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
The paper studies the global convergence of the block Jacobi me\-thod for symmetric matrices. Given a symmetric matrix $A$ of order $n$, the method generates a sequence of matrices by the rule $A^{(k+1)}=U_k^TA^{(k)}U_k$, $k\geq0$, where…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We…
We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
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…
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…
For a general third-order tensor $\mathcal{A}\in\mathbb{R}^{n\times n\times n}$ the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…