Krylov subspace methods have had unparalleled success in solving real-life problems across disciplines ranging from computational fluid dynamics to statistics, machine learning, control theory, and chemistry, among many others. This article provides a brief history of these methods, discussing their origin, expansion, the lives people behind them.

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm i...

This paper presents the use of Inverse Free Krylov Subspace Algorithm (IFKSA) with Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) for the Direction-of-Arrival (DOA) estimation under element failure in a Uniform Linear Antenna Array (ULA). Failure of a few elements results in sparse signal space. IFKSA algorithm is an iterative algorithm to find the dominant eigenva...

The approximate solutions in standard iteration methods for linear systems Ax = b, with A an n by n nonsingular matrix, form a subspace. In this subspace, one may try to construct better approximations for the solution x. This is the idea behind Krylov subspace methods. It has led to very powerful and e$cient methods such as conjugate gradients, GMRES, and Bi-CGSTAB. We will give an overview of...

The study of heat transfer deals with the determination rate energy from one system to another driven by a temperature gradient. It can be observed in many natural phenomena and is often fundamental principle behind several engineering systems. Heat analysis necessary while designing any product. most common numerical method used analyze finite element method. This paper uses demonstrate steady...

GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsymmetric matrix. The method generates a Krylov subspace in which an approximate solution is determined. We present modifications of the GMRES and the closely related RRGMRES methods that allow augmentation of the Krylov subspaces generated by these methods by a user-supplied subspace. We ...