Related papers: GMRES algorithms over 35 years
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
Genetic algorithms, computer programs that simulate natural evolution, are increasingly applied across many disciplines. They have been used to solve various optimisation problems from neural network architecture search to strategic games,…
The main goal of this paper is twofold. First, we extend some results known in the case of weak greedy algorithms with a scalar parameter to the case of weak greedy algorithms with a weakness sequence. Second, we formulate a new setting of…
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…
We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…
In this article we provide a comprehensive review of the different evolutionary algorithm techniques used to address multimodal optimization problems, classifying them according to the nature of their approach. On the one hand there are…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Scheduling problems are generally NP-hard combinatorial problems, and a lot of research has been done to solve these problems heuristically. However, most of the previous approaches are problem-specific and research into the development of…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…