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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

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