Synopsis
Discover a new approach to Monte Carlo problems that aims to improve accuracy with systematic sampling.
This book explains how a non-random method, based on congruences and Weyl’s theorems, can produce faster convergence than traditional random sampling in high-dimensional integrals. It outlines the ideas, the math, and practical implications for problems like chain reactions and other stochastic models.
Opening with the Monte Carlo method, the work then builds a framework for using orderly point sequences in the unit cube. It shows how carefully chosen, linearly independent irrational numbers determine a full sampling scheme and how this can lead to reduced fluctuations in estimates. The discussion spans theory, statistical treatment, and numerical results, with attention to when the improvement is most noticeable.
- How systematic sampling differs from random sampling and when it helps most.
- Connections between uniform distribution, Fourier series, and convergence rates.
- Practical considerations for implementing the method, including error behavior and digits on a machine.
- Numerical examples that illustrate the method’s impact on Monte Carlo calculations.
Ideal for readers of numerical analysis and Monte Carlo methods seeking a rigorous, implementable alternative to standard random sampling.
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Paperback. Condition: New. Print on Demand. This fascinating book proposes a method to enhance Monte Carlo simulations by introducing a new non-random sampling approach grounded in mathematical theories. By replacing the random generation of points in multi-dimensional space with carefully constructed sequences derived from algebraic principles, this method has the potential to yield more accurate results for complex simulations, particularly those with high dimensionality. The author provides theoretical foundations for the method, supported by statistical analysis and numerical examples. The book opens up new avenues for researchers and practitioners seeking to improve the efficiency and precision of their Monte Carlo simulations, a technique widely used in fields such as physics, finance, and engineering. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332421251_0
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