ALAFF Formal derivation of factorization algorithms

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Subsection 5.5.3 Formal derivation of factorization algorithms

In Subsection 3.4.2, we discussed the systematic derivation via the FLAME methodology of Gram-Schmidt algorithms, yielding Classical Gram-Schmidt (CGS) and Modified Gram-Schmidt. LU factorization without pivoting and Cholesky factorization are are straight-forward examples for illustrating the approach [20], [44]. For example, they are discussed in LAFF-On Programming for Correctness, in Week 6 [29], [30].

Whether a family of algorithms for LU factorization with pivoting could similarly be derived had been an open question for decades. It was shown to be within scope of the FLAME methodology in a recent paper [41] that learners in this course may enjoy.