Commentary on Matrix Factorizations and Applications
Nicholas John Higham · Research Explorer (The University of Manchester) · 2007
One of the fundamental tenets of numerical linear algebra is to exploit matrix factorizations. Doing so has numerous benefits, ranging from allowing clearer analysis and deeper understanding to simplifying the efficient implementation of algorithms. Textbooks in numerical analysis and matrix analysis nowadays maximize the use of matrix factorizations, but this was not so in the first half of the 20th century. Golub has done as much as anyone to promulgate the benefits of matrix factorization, particularly the QR factorization and the singular value decomposition, and especially through his book Matrix Computations with Van Loan [28]. The five papers in this section illustrate several different facets of the matrix factorization paradigm.