In this Section we will reconsider the Gaussian elimination approach discussed in HELM booklet 8, and we will see how rounding error can grow if we are not careful in our implementation of the approach. A method called partial pivoting, which helps stop rounding error from growing, will be introduced.
- revise matrices, especially matrix solution of equations
- recall Gaussian elimination
- be able to find the inverse of a matrix
- carry out Gaussian elimination with partial pivoting
2 Partial pivoting
2.1 An example to motivate the idea
2.2 Partial pivoting in general