23 February 1988 Systolic Array For Solving Toeplitz Systems Of Equations
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Abstract
Many problems of geophysics, image processing and time series analysis involve the problem of solving Toeplitz systems of equations. We present a fast parallel 0 (mn) algorithm that solves both square and over-determined Toeplitz systems of equations. The solution is obtained directly from the triangular factorization without using back-substitution. This avoids separate factorization and back-substitution sections, which complicate architectural implementation. This also enables us to eliminate intermediate memory to store the triangular factor. The parallel implementation is carried out in two steps. First, Regular Iterative Algorithms (RIAs) for solving Toeplitz system of equations are formulated systematically from the mathematical description of our algorithm. The advantage of having RIAs is that the process of mapping the algorithms on regular processor arrays can be done in a systematic manner.
© (1988) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
J. Chun, V. Roychowdhury, T. Kailath, "Systolic Array For Solving Toeplitz Systems Of Equations", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); doi: 10.1117/12.948487; https://doi.org/10.1117/12.948487
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