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Matrix Positivity
This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.
Focus on Computational Neurobiology
The most distinctive feature in the development of information science and life science is the gradual and growing interlacing of these two fields. As a result, many new disciplines and technologies have emerged from the overlap of these two areas of science. Today, information science and life science depend on each other so closely that they can no longer exist and grow independently. The interaction and interdependence between the information and life sciences is expected to grow exponentially in the 21st century. Development of the life sciences based on information science and computation will reveal many significant challenges in the life sciences, as well as lead to many new and important discoveries, including targeted and breakthrough drugs. Application of these discoveries extends to such areas as biotechnology, genomics, proteomics, e-health, pharmaceuticals, and the agricultural sciences. Contents: Preface; Applications of Smoothing Methods in Numerical Analysis and Optimisation; Stochastic Programming Models for Vehicle Routing Problems; An Improved Iterative Criterion for GDDM with Elective Parameters; Higher-order Asymptotic Theories of the Jackknife in a Multivariat
Totally Nonnegative Matrices
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow develo...
Mathematical Reviews
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Numerical Methods for Least Squares Problems, Second Edition
The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to...
