Bini, Dario A. Massei, Stefano Robol, Leonardo
Published in
Numerical Algorithms

A quasi-Toeplitz (QT) matrix is a semi-infinite matrix of the kind A=T(a)+E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A=T(a)+E$\end{document} where T(a)=(aj−i)i,j∈ℤ...

Combettes, Patrick L. McDonald, Andrew M. Micchelli, Charles A. Pontil, Massimiliano
Published in
Numerical Algorithms

We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various norms which have been used as regularizers in machine learning, signal processing, and statistics. In particular, the...

Lorin, Emmanuel
Published in
Numerical Algorithms

This paper is devoted to the derivation of a pleasingly parallel Galerkin method for the time-independent N-body Schrödinger equation, and its time-dependent version modeling molecules subject to an external electric field (Bandrauk 1994; Bandrauk et al., J. Phys. B-Atom. Mol. Opt. Phys. 46(15), 153001, 2013; Cohen-Tannoudji et al. 1992). In this g...

Fazzi, Antonio Guglielmi, Nicola Markovsky, Ivan
Published in
Numerical Algorithms

Computing the greatest common divisor of a set of polynomials is a problem which plays an important role in different fields, such as linear system, control, and network theory. In practice, the polynomials are obtained through measurements and computations, so that their coefficients are inexact. This poses the problem of computing an approximate ...

Nowak, Rafał
Published in
Numerical Algorithms

We propose a new simple convergence acceleration method for a wide range class of convergent alternating series. It has some common features with Smith’s and Ford’s modification of Levin’s and Weniger’s sequence transformations, but its computational and memory cost is lower. We compare all three methods and give some common theoretical results. Nu...

Andrei, Neculai
Published in
Numerical Algorithms

A diagonal quasi-Newton updating algorithm is presented. The elements of the diagonal matrix approximating the Hessian are determined by minimizing both the size of the change from the previous estimate and the trace of the update, subject to the weak secant equation. Under mild classical assumptions, the convergence of the algorithm is proved to b...

Kuian, Mykhailo Reichel, Lothar Shiyanovskii, Sergij V.
Published in
Numerical Algorithms

The polynomial interpolation problem with distinct interpolation points and the polynomial represented in the power basis gives rise to a linear system of equations with a Vandermonde matrix. This system can be solved efficiently by exploiting the structure of the Vandermonde matrix with the aid of the Björck–Peyrera algorithm. We are concerned wit...

Wang, Yuan-Ming
Published in
Numerical Algorithms

A high-order Crank-Nicolson-type compact difference method is proposed for a class of time fractional Cattaneo convection-diffusion equations with smooth solutions. The convection coefficient of the equation may be spatially variable. A suitable transformation is adopted to transform the original equation into a reaction-diffusion equation, which i...

Sun, Tao Barrio, Roberto Jiang, Hao Cheng, Lizhi
Published in
Numerical Algorithms

We consider an accelerated proximal gradient algorithm for the composite optimization with “independent errors” (errors little related with historical information) for solving linear inverse problems. We present a new inexact version of FISTA algorithm considering deterministic and stochastic noises. We prove some convergence rates of the algorithm...

Li, Jian Mao, Mingzhi Uhlig, Frank Zhang, Yunong
Published in
Numerical Algorithms

Finite difference schemes have been widely studied because of their fundamental role in numerical analysis. However, most finite difference formulas in the literature are not suitable for discrete time-varying problems because of intrinsic limitations and their relatively low precision. In this paper, a high-precision 1-step-ahead finite difference...