Название: Numerical Mathematics: Systems of Linear Equations, Eigenvalue Problems, Non-Linear Equations
Автор: Martin Hermann
Издательство: De Gruyter
Год: 2026
Страниц: 513
Язык: английский
Формат: epub
Размер: 39.0 MB

Numerical mathematics is one of the cornerstones of the study of mathematics, engineering, physics and computer science. This two-volume textbook is designed for introductory lectures and lays a solid foundation for further learning units. The first volume covers the entire field of numerical mathematics from classical techniques such as the Gaussian algorithm and Newton’s method to modern algorithms such as least squares approximation using Householder and Givens transformations and deflation techniques. The methods are described with mathematical precision, implemented in MATLAB codes and demonstrated using examples. The MATLAB codes are available for download on the publisher’s website so that readers can carry out their own experiments with the numerical methods.

Over the last two decades, a new interdisciplinary field has emerged, known as scientific computing, which lies at the intersection of numerical mathematics, computer science, and the applied sciences. High-performance computers and methods from computer science and numerical mathematics are used here to solve complex problems in the natural sciences and engineering. While traditional science was based on the two pillars of theory and experiment, scientific computing represents the third pillar. Experiments, which are often very expensive, can now be replaced by much cheaper computer simulations. Many research results, such as the decoding of the human genome, the calculation of fundamental physical quantities in particle physics, the further development of electronic components, and modern cancer therapy, would be inconceivable without scientific computing. Numerical mathematics plays a central role in this field. It provides suitable numerical algorithms that are used on modern high-performance computers.

This book aims to familiarize the readers with the basic concepts of numerical computing and provide them with the fundamental techniques and algorithms of numerical mathematics. An important tool in this text are programs written in the MATLAB language. However, they can be easily rewritten so that they can also be used with the noncommercial MATLAB clones SciLab and Gnu Octave. MATLAB provides a numerical computing environment and is one of the fourth-generation programming languages. MATLAB enables manipulation of vectors and matrices, plotting of functions and data, easy implementation of algorithms, and integration of programs written in the computer languages C, C++, Java, or Fortran. A variety of toolboxes are available for specific mathematical problems and applications.

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