Stability of Block $LU$-Decompositions of Matrices Arising from BVP
R.M.M. Mattheij · SIAM Journal on Algebraic and Discrete Methods · 1984
An analysis is made of the stability of block $LU$-decompositions of matrices arising from boundary value problems of ODE. It is based on an investigation of the growth properties of the related recursion (or ODE) solution spaces. It is shown how blocks in the upper right corner or the lower left corner of the matrix may generate blocks in the decomposition that exhibit a growth like some of these solutions, unstable ones not excluded. In particular, for partially separated boundary conditions the desire to reduce memory space may thus conflict with that for actual stability of this decomposition.