"Monte Carlo" Methods for the Iteration of Linear Operations (Classic Reprint) - Hardcover

J. H. Curtiss

9780265920633: "Monte Carlo" Methods for the Iteration of Linear Operations (Classic Reprint)

Hardcover

ISBN 10: 0265920639 ISBN 13: 9780265920633

Publisher: Forgotten Books, 2018

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Monte Carlo Methods for the Iteration of Linear Operators offers a clear, accessible look at a powerful stochastic approach to solving linear problems.

It presents the idea that random sampling can approximate solutions to operator equations, with practical guidance on how to implement and analyze the method.

This edition focuses on two key cases: ordinary integral transforms and matrix-based systems, and it discusses how to set up random walks and Markov chains to estimate unknowns. It also explores variance estimates, convergence conditions, and the role of absorbing states in efficient computation. The text emphasizes a practical path toward applying these ideas, without getting lost in excessive detail about implementation.

How Monte Carlo ideas translate into solving linear equations and operator iterations
How to build and analyze stochastic estimators for specific components or rows
How to create finite, tractable random processes that mirror underlying mathematical models
How to assess and control variance to ensure reliable results

Ideal for readers of mathematical methods, numerical analysis, and stochastic modeling who want a solid, self-contained guide to this important technique.

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