Forward transient electromagnetic modeling requires the numerical solution of a linear constant-coefficient initial-value problem for the quasi-static Maxwell equations. After discretization in space this problem reduces to a large system of ordinary differential equations, which is typically solved using finite-difference time-stepping. We compare standard time-stepping schemes such as the exp...

We show how the quasi-Newton least squares method (QN-LS) relates to Krylov subspace methods in general and to GMRes in particular.

This is the second part in a series of papers on using spectral sparse grid methods for solving higher-dimensional PDEs. We extend the basic idea in the first part [18] for solving PDEs in bounded higher-dimensional domains to unbounded higher-dimensional domains, and apply the new method to solve the electronic Schrödinger equation. By using modified mapped Chebyshev functions as basis functio...

Quaternion non-local means (QNLM) denoising algorithm makes full use of high degree self-similarities inside images to suppress the noise, so similarity metric plays a key role in its performance. In this study, two improvements have been made for QNLM: 1) For low level quaternion quasi-Chebyshev distance is proposed measure image patches and it has used replace Euclidean QNLM algorithm. Since ...

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet-Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of ...

In the paper [8], the author introduced a set of Chebyshev-like points for polynomial interpolation (by a certain subspace of polynomials) in the square [−1, 1], and derived a compact form of the corresponding Lagrange interpolation formula. In [1] we gave an efficient implementation of the Xu interpolation formula and we studied numerically its Lebesgue constant, giving evidence that it grows ...

A new family of AN -type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero–Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin H...

Gradient iterations for the Rayleigh quotient are elemental methods for computing the smallest eigenvalues of a pair of symmetric and positive definite matrices. A considerable convergence acceleration can be achieved by preconditioning and by computing Rayleigh-Ritz approximations from subspaces of increasing dimensions. An example of the resulting Krylov subspace eigensolvers is the generaliz...

A polynomial filtered Davidson-type algorithm is proposed for symmetric eigenproblems, in which the correction-equation of the Davidson approach is replaced by a polynomial filtering step. The new approach has better global convergence and robustness properties when compared with standard Davidson-type methods. The typical filter used in this paper is based on Chebyshev polynomials. The goal of...

In this paper we analyze a class of projection operators with values in a subspace of polynomials. These projection operators are related to the Hubert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthogonality relat...