Noisy Information And Computational Complexity

This book is about the computational complexity of mathematical problems that involve noisy information. The author develops a general theory of computational complexity of continuous problems with noisy information, and provides applications in different settings. He also presents optimal algorithms, optimal information, and complexity bounds in different settings, including worst case, average case, mixed worst-average, and average-worst cases. The book integrates the work of researchers in such areas as computational complexity, approximation theory, and statistics, and includes many fresh results. The book is relevant to computer scientists, statisticians, applied mathematicians, engineers, control theorists, and economists.

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statisticians, applied mathematicians, engineers, control theorists, and economists. Review: The monograph is well organized and carefully written. It serves as an excellent reference book for branch of computational complexity. It is relevant also to statisticians and to applied mathematicians who analyze algorithms for problems for problems with noisy data. Klaus Ritter, Mathematical Reviews