Title: A Theoretical Comparison of the Efficiencies of Two Classical Methods and a Monte Carlo Method for Computing One Component of the Solution of a Set of Linear Algebraic Equations Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 0656029811
ISBN 13: 9780656029815
Binding: HRD
Condition: New
Weight: 403 grams

About this title

Synopsis

How to compute one component of a solution more efficiently

Learn how three different methods compare for solving a set of linear equations, focusing on the work required to get a chosen accuracy.

This study presents a framework to judge Gauss elimination, a particular stationary linear iterative method, and a Monte Carlo method. It shows how the required work scales with the problem size and explains when Monte Carlo can be the better choice, especially as the matrix size grows.

How each method’s workload grows with the matrix order n and the target accuracy
Conditions where Monte Carlo becomes more efficient than classical methods
Upper bounds and break-even points that indicate favorable ranges of n
A new minimum-variance Monte Carlo arrangement designed to reduce variance and speed up solving linear equations

Ideal for readers of numerical analysis and computational mathematics who want a clear, theory-grounded comparison of traditional and stochastic approaches to a common linear-algebra task.

"About this title" may belong to another edition of this title.

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