This second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of the two new chapters are integral equations and mathematical optimization. The book provides alternative solutions to software tools amenable to hand computations to validate the results obtained by "black box" solvers. It also offers an insight into the mathematics behind many CAD, CAE tools of the industry. The book aims to provide a working knowledge of the various approximation techniques for engineering practice.
Table of Contents
Preface. Part I Data approximations. Classical interpolation methods. Approximation with splines. Least squares approximation. Approximation of functions. Numerical differentiation. Numerical integration. Part II Approximate solutions. Nonlinear equations in one variable. Systems of nonlinear equations. Iterative solution of linear systems. Approximate solution of eigenvalue problems. Initial value problems. Boundary value problems. Integral equations. Mathematical optimization.
Dr. Komzsik is a graduate of the Technical University and the Eötvös University of Sciences, both in Budapest, Hungary. He worked for the Hungarian Shipyards in Budapest during the 1970s as an engineering analyst. After immigrating to the U.S., he worked for the McDonnell-Douglas Corporation between 1981-1982 as a senior analyst. Following that, he spent two decades as Chief Numerical Analyst at the MacNeal-Schwendler (now MSC Software) Corporation. After another decade and a half, he recently retired as Principal Key Expert from Siemens PLM Software.
He is the author of the original NASTRAN Numerical Methods Handbook, and a widely read book on The Lanczos Method that was also published in Chinese, Japanese, and Hungarian. His books titled "Computational Techniques of Finite Element Analysis" and "Applied Calculus of Variations for Engineers and Approximation Techniques for Engineers" are already in their second editions. He is also the co-author of the book, "Rotor Dynamics with Finite Elements."