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Exercise 9: An illustration of an analog of algorithm for Cholesky, and the derivation of other analogs for some algorithms.

The Cholesky factorization of a symmetric positive definite matrix A is , where L is a lower triangular matrix. The algorithm is very similar to Gaussian elimination, but the special properties of A mean only half as much storage and half as many flops are needed as for standard Gaussian elimination. Here is the analog of Algorithm 6.1 for Cholesky:

Note that Cholesky does not require pivoting. Derive analogs of Algorithms 6.2 through 6.4 for Cholesky. Ideally your algorithm should only need to read and write the lower (or upper) triangular part of A.