Numerical Analysis I, Fall 2011 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 09

Assigned Nov 11, 2011.

1. Section 6.6: Problems 17, 20, 21, 25.

2. Denote by A_{k} the k × k leading principle of A. Show that if A_{k} = L_{k}U_{k} with L_{k} unit lower triangular ((L_{k})_{ii} = 1) and U_{k} upper triangular, then det(A_{k}) = det U_{k}. Use it to prove Theorem 6.24 (except the stable part).

3. Preview Algorithms 6.5, 6.6 and 6.7. We will explain them and talk about implementation next week.