A Non-Random Sampling Method (Classic Reprint) - Softcover

Richtmyer, Robert D.

Softcover

ISBN 10: 1332421253 ISBN 13: 9781332421251

Verlag: Forgotten Books, 2018

Inhaltsangabe

Excerpt from A Non-Random Sampling Method

During the past ten years, several studies have been made of systematic (non-random) sampling methods, for calculations of the monte Carlo type, based on theorems of H. Weyl[l] on the asymptotic distribution, in n-space, of a set of points generated by congruences. The object is to find a computing method, similar to monte Carlo, in which the error of the approximation decreases more rapidly, with increasing sampie size, than when random sampling is used. Although the method has not yet achieved success in practical applications, there seems to be enough interest in it to warrant giving an account.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Über diesen Titel

Reseña del editor

Excerpt from A Non-Random Sampling Method

Unfortunately, the theorems referred to are not broad enough to be applicable to practical Monte Carlo problems because of the restriction to k l in Ostrowski's theorem and to very smooth integrands in the theorems of the writer and of Peck. A new approach to the problem is therefore taken, in Section 4, by reintroducing statistical considerations. If, at the beginning of a problem, the numbers gk are chosen at random from some continuous distribution, then, with exception of choices having probability zero, they will indeed turn out to be linearly independent irrational numbers. We can therefore regard the gk as random variables (they will be taken to have a uniform distribution in the unit cube, since there is no loss of generality in this choice); for given N (and a given function IN is then a function of the random variables gk, and we may discuss its statistics.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1332421253
• ISBN 13: 9781332421251
• Einband: Tapa blanda
• Anzahl der Seiten: 54
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar