Analysis of new pivoting strategy for the LDLT decomposition on a multiprocessor system with distributed memory

It is well known that optimal control techniques can provide the ability to design suitable strategies, however, the on-line computing requirements are excessive. The normal procedure is to make various assumptions so that the processing demands are reduced. Based on these assumptions, sequences of linear-quadratic-performance optimal control problems need to be considered. These in turn give rise to standard two-point-boundary-value problems. The solution to such problems involves computation of algebraic Riccati equations (AREs). The block diagonal decomposition LDL^T, is the key step for those algorithms based on the matrix sign function that are used in solving AREs. The last few years have witnessed a tremendous effort towards the development of reliable algorithms to solve AREs and apply it in industrial situations. However, all implementations and testing of the proposed algorithms have been performed on powerful machines thereby limiting their practical application. The authors present a pivoting strategy that: (i) requires only one-dimension of the matrix for selection of the pivot; (ii) generates regular communication patterns; and (iii) establishes a software mechanism for the development of fault tolerant applications. The results obtained from a multiprocessor system with a one-way ring topology indicate that block diagonal LDL^T decomposition is a true candidate for real-time use and fault tolerant applications and also as a framework-test for the LAPACK library.