review1.dvi
ECS130 Midterm I Review Checklist
1. Tools of the trade:
• matrix-matrix multiplication in different ways
• BLAS
• vector and matrix norms, ‖ · ‖1, ‖ · ‖2, ‖ · ‖F , ‖ · ‖∞.
2. Floating-point arithmetic
• Floating point representation of numbers
• IEEE floating-point numbers, single and double precision
• Rounding modes and errors
• Floating-point arithmetic
• Catastrophic cancellation
3. Lower and upper triangular linear systems
row-majored or column-majored
componentwise or vecctorized
4. Gaussian Elimination = LU factorization with pivoting
PA = LU
The need of pivoting, mathematically and numerically
Cholesky decomposition of a symmetric positive definite matrix
Applications:
• solve Ax = b
• solve AX = B, where B is a n× p matrix
• compute A−1
5. Error analysis for a computed solution of Ax = b.
Rule of thumb:
relative forward error ≤ condition number× relative error in b
1