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.

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