## New Parallel Algorithms for Direct Solution of Linear EquationsSystems of linear equations arise frequently in engineering systems analysis, and methods of solving these systems are an increasing area of research required to improve speed, fault tolerance, and scalability. This book presents new research in the area of solving linear equations. Readers will find that instead of "parallelizing" the usual algorithms, the authors have developed new ones. |

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algorithm based algorithm for solving b-vector back substitution phase backward direction backward matrix BFSP BGE algorithm bidirectional algorithm bidirectional elimination algorithms bisection width block partitioning broadcast BSCF algorithm checksum Cholesky factorization coefficient matrix column update operations communication denotes efficient elim error forward and backward forward direction forward elimination Gaussian elimination Givens rotations Gram-Schmidt orthogonal Householder reductions hypercube implementation K. N. Balasubramanya Murthy linear equations linear system log N stages LU decomposition LU factorization mesh method modifies column multiplier column multiprocessor node nonpivot column processor nonpivot column update number of processors numerical stability obtained orthogonal matrix pairwise pivoting parallel algorithm Parallel Computing PARBEGIN PAREND partial pivoting perform permutation network pivot column processor problem reduced semirings sequential algorithm Siva Ram Murthy solution of linear solution vector sparse symmetric step subdiagonal subdiagonal elements submatrix system of linear trapezoidal triangular matrix triangular system upper triangular