Linear Algebra Methods
- Gaussian elimination, \( O(2/3n^3) \) flops, general matrix
- LU decomposition, upper triangular and lower tridiagonal matrices, \( O(2/3n^3) \) flops, general matrix. Get easily the inverse, determinant and can solve linear equations with back-substitution only, \( O(n^2) \) flops
- Cholesky decomposition. Real symmetric or hermitian positive definite matrix, \( O(1/3n^3) \) flops.
- Tridiagonal linear systems, important for differential equations. Normally positive definite and non-singular. \( O(8n) \) flops for symmetric. Special case of banded matrices.
- Singular value decomposition
- the QR method will be discussed in chapter 7 in connection with eigenvalue systems. \( O(4/3n^3) \) flops.