The CMSSL library only includes a limited amount of mathematical algorithms. Hence, when writing code for the Connection Machine one often has to implement LAPACK-style routines already developed for other architec-tures, in the hope that acceptable performance can thus be obtained relatively quickly. Due to the massively parallel structure of the CM, algorithms with a serial or global structur...

In this paper we introduce the multiresolution LU factorization of non-standard forms (NS-forms) and develop fast direct multiresolution methods for solving systems of linear algebraic equations arising in elliptic problems. The NS-form has been shown to provide a sparse representation for a wide class of operators, including those arising in strictly elliptic problems. For example, Green’s fun...

This paper gives sensitivity analyses by two approaches for L and U in the factor-ization A = LU for general perturbations in A which are suuciently small in norm. By the matrix-vector equation approach, we derive the condition numbers for the L and U factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete pivoting aaect th...

The concept of block{cyclic order elimination can be applied to out{of{ core LU and QR matrix factorizations on distributed memory architectures equipped with a parallel I/O system. This elimination scheme provides load balanced computation in both the factor and solve phases and further optimizes the use of the network bandwidth to perform I/O operations. Stability of LU factorization is enfor...

The solution of nearly square overdetermined linear systems is studied. The sparse QR technique is compared with two sparse LU-based techniques. Numerical tests with realworld and artificial matrices indicate that the LU techniques are more accurate for incompatible right-hand sides. Also, the amount of floating point operations required by LU techniques is approximately one half smaller than Q...

This paper discusses some relationships between Incomplete LU (ILU) factoriza-tion techniques and factored sparse approximate inverse (AINV) techniques. While ILU factorizations compute approximate LU factors of the coeecient matrix A, AINV techniques aim at building triangular matrices Z and W such that W > AZ is approximately diagonal. The paper shows that certain forms of approximate inverse...