For the direct solution of tridiagonal linear systems Ax = d, the best known serial algorithm is based on LU-factorization of the coefficient matrix A. In the present paper we consider extending the idea to partitioned tridiagonal matrices. Let A be partitioned: A = (A (i, j)) so that the diagonal blocks A( i,i )are tridiagonal. We seek a factorization of A into L = (L (i j) and U = (U (i j) ), partitioned conformally. For the diagonal blocks of A we require the classical factorization: A( ii ) = L (i,i) U (i,i) , L (i,i) unit lower bidiagonal and U (i,i) upper bidiagonal. But, because of the presence of a non-zero element in each of the off-diagonal blocks of A, it is necessary to have Lupper block bidiagonal and U lower block bidiagonal, with only last row of L(i,i+1) and last column of U(i,i-1) filled. To avoid any interlocking/updating during/after the factorization stage, each of these last row and column in each block are required to have their last elements as zeros. On completion of the determinat...

A direct incomplete factorization method for parallel solution of tridiagonal linear systems

Fitted diagonals for reducing I/O bandwidth in systolic systems

Parallel Non-Linear Algorithms

We are witnessing a great number of modifications in the computing systems that are designed, built and available to the community. Not all of these changes are radical and some are only technical, yet it may be important to trace back the origins of these changes and, if possible, predict the future trends, particularly within the field domain of this Institute: spatially distributed data analysis.

One, Two,… Many Processors for Image Processing

Evans [2, 3] introduced the method of recursive point partitioning algorithm for the solution of sparse banded matrix systems and investigated the “one-line at a time” strategy for the solution of tridiagonal linear systems. Recursive block partitioning schemes resulting from variation in the size of the block structure using “two-lines at a time” have been investigated for both the tridiagonal and the quindiagonal matrix systems in Okolie [6]. The case of partitioning strategy for an nth order system has been considered by Evans and Okolie [4] resulting in a recursive decoupling algorithm for tridiagonal linear systems. Following the recursive point partitioning algorithm of Evans [2, 3], Chawla et al [1] developed a recursive partitioning algorithm for inverting tridiagonal matrices. In the present paper we present a method for inverting tridiagonal matrices by adopting the strategy resulting in a recursive doubling algorithm; the present algorithm has a highly parallel structure.

A recursive doubling algorithm for inverting tridiagonal matrices

Parallel Processing Systems

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Parallel Processing Systems

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A direct incomplete factorization method for parallel solution of tridiagonal linear systems

Fitted diagonals for reducing I/O bandwidth in systolic systems

Parallel Non-Linear Algorithms

One, Two,… Many Processors for Image Processing

A recursive doubling algorithm for inverting tridiagonal matrices

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