相关论文: Vandermonde with Arnoldi

This paper presents a methodology to construct a divergence-free polynomial basis of an arbitrary degree in a simplex (triangles in 2D and tetrahedra in 3D) of arbitrary dimension. It allows for fast computation of all numerical solutions…

We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…

The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…

We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue…

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…

The Sanathanan-Koerner iteration developed in 1963 is classical approach for rational approximation. This approach multiplies both sides of the approximation by the denominator polynomial yielding a linear problem and then introduces a…

Arnoldi method and conjugate gradient method are important classical iteration methods in solving linear systems and estimating eigenvalues. Their efficiency often affected by the high dimension of the space, where quantum computer can play…

This paper presents a self-contained factorization for the Vandermonde matrices associated with true-time delay based wideband analog multi-beam beamforming using antenna arrays. The proposed factorization contains sparse and orthogonal…

This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…

We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast…

Quadratization problem is, given a system of ODEs with polynomial right-hand side, transform the system to a system with quadratic right-hand side by introducing new variables. Such transformations have been used, for example, as a…

A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…

In this note we present a parameterized class of lower triangular matrices. The components of the eigenvectors grow rapidly and will exceed the representational range of any finite number system. The eigenvalues and the eigenvectors are…

We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem, some forms of which are the vector M-Pad\'e approximation problem in [Van Barel and…

In recent years, a great deal of attention has been focused on numerically solving exponential integrators. The important ingredient to the implementation of exponential integrators is the efficient and accurate evaluation of the so called…

Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…

We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…

We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares (IRLS) algorithm, a saddle-escaping smoothing Newton method or a variable metric proximal gradient method…