Factored form of basis

From Glossary

Jump to: navigation, search

Originally for linear programming, this pertains to writing a basis LaTeX: B in the form, LaTeX: B = F_1 F_2 ... F_k , where LaTeX: F_i are factors. Two forms of interest are: elementary factors, where each LaTeX: F_i is an elementary matrix, and LU decomposition: LaTeX: B=LU, where LaTeX: L is lower triangular and LaTeX: U is upper triangular. (LaTeX: L and LaTeX: U might be factored, notably into elementary matrices, which are lower and upper triangular, resp.) These have inexpensive updates when LaTeX: B changes to an adjacent basis.

Personal tools