Lecture 4 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Solution of large linear systems
  • Condition such that the system has a unique solution
  • Do not compute the inverse of matrix A
  • Method of choice for direct solver is an LU decomposition
  • Floating point numbers, rounding errors, disasters caused by numerical errors
  • Machine precision, cancellation
  • Floating point calculation of an inner product
  • Matrix and vector norms
  • Absolute and relative error
  • Multiplicative matrix norm, associated matrix norm
  • Various matrix norms
  • Rounding errors in linear systems
    
    
• Material is described in pages 8 - 11, and 41 - 43 of the lecture notes. Recommended exercises: 2.12.1 - 2.12.10, 2.12.13, 2.12.14, 2.12.17, 2.12.18