engleski

Numerical methods II - Roots and Equation Systems

The series of books Numerical Methods are written primarily for the students at technical universities, but also as a useful handbook for engineers and PhD students. This textbook introduces the reader into various root finding methods as well as into methods for solving linear equation systems and series of such systems along with minimising computation time, minimizing 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 root finding methods and methods for solving linear equation systems are already implemented in the calculators and standard computer libraries, providing their instant use. However, the use of described methods gives an opportunity to the reader to take a fool control over computation, and 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. Chapters. The book is divided into four chapters. In the first chapter, the two classes of general iterative root finding methods, i.e. open methods and close methods, are briefly explained. These methods can be used for finding roots of nonlinear equations as well as a solution 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 memory sparing sequential substitution method (SS), which is the background for the sequentially elimination method (SEM) (described in the third chapter) and the improved sequential substitution method (ISS) (described in the forth chapter). These memory sparing methods are direct methods for solving linear equation systems that use much less memory than standard methods, and sometimes even less memory than iterative methods. The SEM is further optimised for solving linear equation systems with populated system matrix while the ISS is a more general method optimised for solving linear equation systems with sparse system matrix as well as series of linear equation systems. There is also possibility to calculate only selected unknowns, and in that way to remarkably reduce a number of numerical operations and an amount of used computer memory. Practical application is supported by 37 examples, 51 algorithms (including SEM and ISS) and 23 flowcharts. Algorithms are written in pseudo-code, FORTRAN or C so that they can be easily included into any computer program. Besides its practical application, the given text with 46 figures and 20 tables, partially in colour, represents a valuable background for understanding, using, developing and applying various numerical methods.

numerical methods; rooths; solving linear equation systems

Knjiga ima dva izdavača. Knjiga je razvrstana kao znanstvena. Pored toga službeni je sveučilišni udžbenik Sveučilišta u Rijeci, Fakultete za Logistiko Univese v Mariboru i Moscow State Industrial Universiti