Numerical Linear Algebra

模块目标

Distinguish a mathematically unique solution from a numerically reliable computation, and quote backward-error or residual bounds when the synopsis does.

课程大纲

1. 01 Norms and condition numbers 20h

   学习结果 Compute or bound a condition number and interpret it as sensitivity, not as a residual.

   形成性检查 四选一检查

2. 02 LU and pivoting 25h

   学习结果 State when LU exists, what pivoting changes, and a case where naive LU fails.

   形成性检查 反例

3. 03 QR and least squares numerically 25h

   学习结果 Relate QR to least squares and contrast it with forming AᵀA when A is ill-conditioned.

   形成性检查 书面推导

4. 04 Residual versus forward error 20h

   学习结果 Give an example with a small residual and a large forward error.

   形成性检查 反例

5. 05 Iterative methods (taught grain) 25h

   学习结果 State an iteration, a contraction or residual monitor, and a stopping caveat.

   形成性检查 书面推导

6. 06 Eigenvalue computations (introduction) 15h

   学习结果 Name a method at synopsis grain and a stability issue for non-normal matrices.

   形成性检查 四选一检查

7. 07 Synthesis 20h

   学习结果 Choose a factorisation or iteration for a stated system and justify the choice by conditioning.

   形成性检查 书面推导

学习结果

Describe LU/QR or an iterative method with an operation count and a stability or residual caveat.

学科技能

Matrix factorisations, condition numbers, residual vs error, iterative methods at taught grain.

可迁移技能

Report a residual; refuse to treat floating-point output as exact algebra.