Chapter 15

Cholesky Factorization

Section 8.8 used matrix multiplication to introduce the notion of recursive linear algebra and cache-oblivious algorithms, based on the fork–join pattern. The Cholesky decomposition example here shows how the pattern applies to parallelizing other operations in dense linear algebra, even when the matrices are triangular. The chapter also gives a brief introduction to the art of using Fortran-oriented BLAS routines in C/C++. Though the algorithms apply to large matrices, all you have to know is algebra on 2 × 2 matrices to understand how they work.

15.1 Fortran Rules!

The matrix layout used in the Cholesky routine and subsidiary routines is column-major, just like Fortran, not as usual in C/C++, so the layout will ...

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