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lect03

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lect03, Tue 01/14

Solving Ax=b by LU factorization

• Lecture Files

Reading assignment for next lecture

Read NCM Problem 2.5 (Cholesky factorization) and Section 5.5 (QR factorization), and the first two sections (Introduction and Computation) of Nick Higham’s writeup of Cholesky factorization.

References for today’s lecture

NCM Sections 2.1 through 2.6 (linear equations and Gaussian elimination).

Outline

• This week’s big idea: Matrix Factorizations

• Interesting matrices:
  • Triangular matrices
  • Unit triangular matrices
• Solving Ax = b by LU factorization:
  • Residual b - Ax, residual norm
  • Solving triangular systems
  • Gaussian elimination
  • LU factorization
  • Partial pivoting
• numpy/scipy routines:
  • npla.matrix_rank()
  • npla.norm()
  • npla.cond()
  • npla.solve()
  • spla.lu()
• Lecture codes:
  • LUfactor()
  • Lsolve()
  • Usolve()