Lecture 5 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Condition of a matrix, perturbation of right-hand side vector
  • perturbation of matrix and a combination with right-hand side perturbation
  • Definition of lower and upper triangular matrix L and U
  • How to compute L and U for a simple example
  • Solve LU u = f
  • Lower and upper triangular solve
  • General definition of the LU decomposition
  • Gauss transformation, Gauss vector
  • Inverse of a Gauss transformation, link Gauss transformations with L
  • Products of Gauss transformations
  • Memory and storage for L and U
  • Number of floating point operations for LU decomposition
  • Rounding error analysis of the LU decomposition
    
    
• Material is described in pages 43 - 52 of the lecture notes. Recommended exercises: 4.13.1 - 4.13.4
  
  
• Typo's
  
  
  • Page 45: third line of section 4.3.3, "with a diagonal matrix" should be "with the inverse of a diagonal matrix"