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Systolic algorithms for the parallel solution of dense symmetric positive-definite Toeplitz systems. Research report

Technical Report ·
OSTI ID:6267353
The most popular method for the solution of linear systems of equations with Toeplitz coefficient matrix on a single processor is Levinson's algorithm, whose intermediate vectors form the Cholesky factor of the inverse of the Toeplitz matrix. However, Levinson's method is not amenable to efficient parallel implementation. In contrast, use of the Schur algorithm, whose intermediate vectors form the Cholesky factor of the Toeplitz matrix proper, makes it possible to perform the entire solution procedure on one processor array in time linear in the order of the matrix. By means of the Levinson recursions it is shown that all three phases of the Toeplitz system solution process - factorization, forward elimination; and backsubstitution - can be based on Schur recursions. This increased exploitation of the Toeplitz structure then leads to more-efficient parallel implementations on systolic arrays.
Research Organization:
Yale Univ., New Haven, CT (USA). Dept. of Computer Science
OSTI ID:
6267353
Report Number(s):
AD-A-182633/8/XAB; YALEU/DCS/RR-539
Country of Publication:
United States
Language:
English

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