On the \(LU\) factorization of infinite systems of semi-separable equations
Closed and canonical expressions for the \(LU\) factors and related existence theorems and factorization algorithms for the case where the original system is invertible and the factors are required to have inverses as the same type as themselves. The author focuses on \(LU\) factorization in the context of infinitely indexed systems. The main tool used is canonical forms. The resulting algorithm is independent of the existence of the solution and has, in addition, the very nice property that it only uses orthogonal transformations. It is shown that the computation of subsequent partial Schur complements is numerically stable.
scientific article; zbMATH DE number 6112941
scientific article