Numerical Methods II - Roots and Equation Systems

Paperback, color print on 70lb white paper. Other e- and printed color and b&w editions are or will be also available. * * * About the book: An excellent textbook established at several universities. Primarily written for students at technical universities, it is also a very useful handbook for engineers, PhD students and scientists. Now available at all continents. - - - This textbook introduces the reader into various root finding methods and into methods for solving linear equation systems and series of such systems, along with the minimisation of computation time, required memory and selective computation of only required unknowns. - - - These methods are important because there are many problems in engineering practice and science that cannot be solved without them. Some methods are already implemented in calculators and standard program libraries, providing their instant use. However, the use of the described methods gives an opportunity to the reader to take full control over computation, and to apply the method which is most suitable for solving his problem. This approach can make numerical algorithms more powerful and faster than they used to be. - - - The book has four chapters. In the first chapter, the open and the bracketing root-finding methods are briefly explained. They can be used for finding roots of nonlinear equations as well as solutions of nonlinear equation systems. In the second chapter, various standard methods for solving linear equation systems, inversion of matrices and calculation of determinants are described. There is also the memory sparing sequential substitution method (SS), which is the background for the sequential elimination method (SEM) (the third chapter) and the improved sequential substitution method (ISS) (fourth chapter). These direct methods use much less memory than the standard methods, and sometimes even less memory than iterative methods. The SEM is further optimised for solving systems with populated system matrix while the ISS is a more general method optimised for solving systems with sparse system matrix as well as series of systems. There is also the possibility to calculate only the selected unknowns, and in that way to remarkably reduce the number of numerical operations and the amount of used computer memory. - - - Practical application of the described methods is supported by 37 examples, 23 flowcharts, 51 algorithms and several computer programs written in Fortran and C that can be immediately implemented for any application. In addition to its practical usage, the given text with 46 figures and 20 tables represents a valuable background for understanding, using, developing and applying various numerical methods. * * * Author: Boris Obsieger, D.Sc., professor at the University of Rijeka, Croatia. Head of Section for Machine Elements at the Faculty of Engineering in Rijeka. Holds lectures on Machine Elements Design, Robot Elements Design, Numerical Methods in Design and Boundary Element Method. Several invited lectures. President of CADAM Conferences. Main editor of international journal Advanced Engineering. Author of several books and a lot of scientific papers. * * * Reviewed by: Prof. Maja Fosner, D.Sc., University of Maribor, Slovenia; Prof. Damir Jelaska, D.Sc., University of Split, Croatia; Prof. Valery Lysenko, D.Sc., Academic of the Russian Metrological Academy, Russian Research Institute for Metrological Service; Prof. Iztok Potrc, D.Sc., University of Maribor. Slovenia; Prof. Evgeny Pushkar, D.Sc., Member correspondent of the Russian Academy of Natural Sciences, Moscow State Industrial University, Russia. * * * Proof reading by: Senior Lecturer, Ksenija Mance, prof., University of Rijeka, Croatia.