Ch06-3 Linear Systems of Equations, Matrix...

38
Ch06-3 Linear Systems of Equations, Matrix Factorization Dr. Feras Fraige

Transcript of Ch06-3 Linear Systems of Equations, Matrix...

Page 1: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.

Ch06-3 Linear Systems of Equations, Matrix Factorization

Dr. Feras Fraige

Page 2: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.

Outline

1 Computation Cost Rationale & Basic Solution Strategy

2 Constructing the Matrix Factorization 3 Example: LU Factorization of a 4 × 4 Matrix 4 The LU Factorization Algorithm 5 Permutation Matrices for Row Interchanges

Page 3: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 4: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 5: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 6: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 7: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 8: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 9: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 10: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 11: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 12: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 13: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 14: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 15: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 16: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 17: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 18: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 19: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 20: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 21: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 22: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 23: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 24: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.

Discuss algorithm

Page 25: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 26: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 27: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 28: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 29: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 30: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 31: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 32: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 33: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 34: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 35: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 36: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 37: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.
Page 38: Ch06-3 Linear Systems of Equations, Matrix Factorizationfac.ksu.edu.sa/sites/default/files/ch06-3_matrix...Part (b) Solution (2/3) First, solve Ly = b (where y — 0 1 Ly _ 4 3 Ux.