TY - BOOK
T1 - A history of Krylov of product methods
T2 - A case of serendipity
AU - Sonneveld, Peter
PY - 2017
Y1 - 2017
N2 - In about 1976, the author was preparing a renovation of the elementary course on numerical analysis in Delft University. In relation to the problem of solving a single non-linear equation iteratively, he wondered whether the so-called ‘secant method’ could be generalized to systems of N nonlinear equations with N unknowns. Before starting to read everything on the subject, the author normally tries to think about it unbiased, and so he did this time, and started with (probably) re-inventing the wheel. Would he have seen the book by Ortega and Rheinboldt at that time, he wouldn’t have discovered the ‘new wheel’ IDR, and also CGS and BiCGSTAB probably wouldn’t exist today. Serendipity means something like ‘finding the unsought’, and the strange history of the socalled ‘Krylov Product methods’ shows some examples of this phenomenon.
AB - In about 1976, the author was preparing a renovation of the elementary course on numerical analysis in Delft University. In relation to the problem of solving a single non-linear equation iteratively, he wondered whether the so-called ‘secant method’ could be generalized to systems of N nonlinear equations with N unknowns. Before starting to read everything on the subject, the author normally tries to think about it unbiased, and so he did this time, and started with (probably) re-inventing the wheel. Would he have seen the book by Ortega and Rheinboldt at that time, he wouldn’t have discovered the ‘new wheel’ IDR, and also CGS and BiCGSTAB probably wouldn’t exist today. Serendipity means something like ‘finding the unsought’, and the strange history of the socalled ‘Krylov Product methods’ shows some examples of this phenomenon.
KW - Iterative methods
KW - IDR
KW - Krylov-subspace methods
KW - Bi-CGSTAB
KW - CGS
KW - nonsymmetric linear systems
M3 - Report
T3 - Reports of the Delft Institute of Applied Mathematics
BT - A history of Krylov of product methods
PB - Delft University of Technology
CY - Delft
ER -