Banert, Sebastian Boţ, Radu Ioan Csetnek, Ernö Robert
Published in
Numerical Algorithms

We investigate the techniques and ideas used in Shefi and Teboulle (SIAM J Optim 24 (1), 269–297, 2014 ) in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM algorithm that is able to handle convex optimizat...

Piersanti, Paolo Shen, Xiaoqin
Published in
Numerical Algorithms

In this paper, a finite element analysis to approximate the solution of an obstacle problem for a static shallow shell confined in a half space is presented. To begin with, we establish, by relying on the properties of enriching operators, an estimate for the approximate bilinear form associated with the problem under consideration. Then, we conduc...

Leriche, E. Labrosse, G.
Published in
Numerical Algorithms

The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied wit...

Gautschi, Walter
Published in
Numerical Algorithms

The first equation in Eq. (2.9) should read

Castellini, Jacopo
Published in
Numerical Algorithms

In this work, we are presenting an efficient way to compute the geometric mean of two positive definite matrices times a vector. For this purpose, we are inspecting the application of methods based on Krylov spaces to compute the square root of a matrix. These methods, using only matrix-vector products, are capable of producing a good approximation...

Le Ferrand, Hervé
Published in
Numerical Algorithms

We explain in this article how the famous Belgian astronomer and physicist Georges Lemaître, a specialist in the theory of relativity, rediscovered, during the Second World War from Gauss’ work, Aitken’s Δ2 process. He called his discovery the rational iteration method and used it to solve an ordinary differential equation. After giving some histor...

Beccari, Carolina Vittoria Casciola, Giulio Mazure, Marie-Laurence
Published in
Numerical Algorithms

This work concerns the useful and large class of all piecewise Chebyshevian splines, in the sense of splines with pieces taken from different Extended Chebyshev spaces all of the same dimension, and with connection matrices at the knots. The subclass of those which are interesting for applications, and in particular for design, is known to be chara...

Liang, Maolin Zheng, Bing Zhao, Ruijuan
Published in
Numerical Algorithms

Recently, the alternating direction method of multipliers (ADMM) and its variations have gained great popularity in large-scale optimization problems. This paper is concerned with the solution of the tensor equation Axm−1=b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{...

Brezinski, Claude Redivo–Zaglia, Michela
Published in
Numerical Algorithms

In this paper, we trace back the genesis of Aitken’s Δ2 process and Shanks’ sequence transformation. These methods, which are extrapolation methods, are used for accelerating the convergence of sequences of scalars, vectors, matrices, and tensors. They had, and still have, many important applications in numerical analysis and in applied mathematics...

Meurant, G.
Published in
Numerical Algorithms