Michela Redivo-Zaglia - Böcker

This expansive volume describes the history of numerical methods proposed to solve linear algebra problems,, from antiquity to the present day. The authors focus on methods for solving linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of the main important contributors to the field.A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, and to applied mathematiciansas well as to and historians of mathematics as well.

The shape of the Earth was a significant scientific question in the eighteenth century. When it was discovered that the Earth was flattened at the poles, scientists sought to understand the cause, leading to the study of the gravitational attraction of celestial spheroids. The solution drew upon Newton’s law of universal gravitation, which used the distance between two bodies based on the law of cosines. Expanding the inverse of this distance into a power series naturally leads to a class of orthogonal polynomials. These were introduced by Legendre and, a little bit later, by Laplace. Legendre was the first to prove their orthogonality. Thirty years later, Gauss, approaching the problem from the perspective of numerical quadrature, independently arrived at the same polynomials. Over time, as concern for the gravitational problem of spheroids waned, the intrinsic mathematical interest in orthogonal polynomials took precedence.The Birth and Early Developments of Orthogonal Polynomials: A Chronological History is the first book to describe the history of orthogonal polynomials, covering their birth and early developments from the end of the 18th century to the middle of the 20th century. It includes biographies of principal and lesser-known figures, anecdotes, and accounts of the countries and institutions involved.The book will appeal to researchers and students in applied mathematics, mathematical analysis, special functions, and orthogonal polynomials as well as to those interested in the history of mathematics and the sciences.

This book paints a fresco of the field of extrapolation and rational approximation over the last several centuries to the present through the works of their primary contributors.