Lecture

Richardson Method: Preconditioned Iterative Solvers

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Description

This lecture covers the Richardson method for solving linear systems, focusing on preconditioned iterative solvers. It explains the concept of preconditioning, the Richardson iteration, and the convergence properties of the method. The lecture also introduces the gradient method and its application in solving linear systems.

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Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

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Preconditioner

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In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

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In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .

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