- Exponentiating by squaring. Quickly computes powers of numbers and matrices.
- Rutishauser. Algorithm for tridiagonalizing banded matrices. Uses the standard chasing step.
- Strassen algorithm. Faster matrix multiplication.
- Symbolic Cholesky decomposition. Efficient way of storing sparse matrix.
- Zha's algorithm. For tridiagonalizing arrowhead matrices, improves Rutishauser.
- Matrix chain multiplication. Given a sequence of matrices, we want to find the most efficient way to multiply these matrices together using dynamic programming (not to perform the multiplication).
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