title: Numerical Methods For Mathematics, Science, and Engineering
author:  John H. Mathews 
description: This introduction to numerical analysis shows how the mathematics of calculus and linear algebra are implemented in computer algorithms.
zlib_text: # Part 1  
  Numerical Methods
  
  
  Philipp O.J. SchererGraduate Texts in PhysicsComputational Physics2nd ed.
  2013Simulation of Classical and Quantum Systems10.1007/978-3-319-00401-3_1©
  Springer International Publishing Switzerland 2013
  
  # 1\. Error Analysis
  
  Philipp O. J. Scherer1
  
  (1)
  
  Physikdepartment T38, Technische Universität München, Garching, Germany
  
  Abstract
  
  Input data as well as the results of elementary operations have to be
  represented by machine numbers, the subset of real numbers which is used by
  the arithmetic unit of today’s computers. Generally this generates rounding
  errors. This kind of numerical error can be avoided in principle by using
  arbitrary precision arithmetics or symbolic algebra programs. But this is
  unpractical in many cases due to the increase in computing time and memory
  requirements. Results from more complex operations like square roots or
  trigonometric functions can have even larger errors since series expansions
  have to be truncated and iterations accu