{"product_id":"9780387985541","title":"Random and Quasi-Random Point Sets","description":"This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen­ erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical (\"a priori\") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional \"random\" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver­ gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These \"quasi-random\" points are produced by deterministic algorithms and should be as \"super\"­ uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":47013089607920,"sku":"9780387985541","price":139.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780387985541_p0.jpg?v=1763696454","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780387985541","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}