Abstract
The VLSI implementation of the Accelerated Overrelaxation (AOR) method, when used for the accurate computation of the least-squares solutions of overdetermined systems, is the problem addressed here. As the size of this computational task is usually very large, we use space-time domain expansion techniques to partition the computation and map it onto a fixed size VLSI architecture.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
J.H. Argyris and O.E. Brönlund, "The natural factor formulation of the stiffness matrix displacement method", Comput. Meth. Appl. Mech. Engrg. 5: 97–119, 1975.
J.H. Argyris, T.L. Johnson and H.P. Mlejnek, "On the natural factor in nonlinear analysis", Ibib. 15: 389–406, 1978.
S.C. Chen, D.J. Kuck and A.H. Sameh, "Practical Parallel Band Triangular System Solvers", ACM Trans. Math. Software, Vol. 4, No. 3, pp. 270–277, Sept. 1978.
Y.T. Chen, "Iterative methods for linear least-squares problems", Ph.D. Dissertation, Univ. of Waterloo, Canada, 1975.
H.D. Cheng and K.S. Fu, "Algorithm partition and parallel recognition of general context free languages using fixed size VLSI architecture", June 1984, Purdue University.
H.D. Cheng and K.S. Fu, "VLSI architectures for pattern matching using space-time domain expansion approach", October 1984, Purdue University.
H.D. Cheng and K.S. Fu, "Algorithm partition for a fixed size VLSI architecture using space-time domain expansion", Proc. 7th Symp. Comput. Arithmetic, June 1985, pp. 126–132.
H.D. Cheng, W.C. Lin and K.S. Fu, "Space-time domain expansion approach to VLSI and its application to hierarchical scene matching", IEEE Trans. on Pattern Anal. Mach. Int., March 1985.
G.H. Golub and R.J. Plemmons, "Large scale geothetic least squares adjustments by dissection and orthogonal decomposition", Linear Algebra and Appl., 34: 3–28, 1980.
A. Hadjidimos, "Accelerated Overrelaxation Method", Math. Comp. 32: 149–157, 1978.
K. Hwang and Y.H. Cheng, "Partitioned algorithms and VLSI structures for large-scale matrix computations", Proc. 5th Symp. Comput. Arithmetic, May 1981, pp. 222–232.
K. Hwang and Y.H. Chen, "Partitioned Matrix Algorithms for VLSI Arithmetic Systems", IEEE Trans, Comp., C-31 (12): 1215–1224, 1982.
I. Kaneco, M. Lawo and Thieraut, "On computational procedures for the force method", Intern. J. Num. Meth. Eng. 18: 1469–1495, 1982
C.B. Kolata, "Geodecy: dealing with an enormous computer task", Science, 200: 421–422, 1978.
D.I. Moldovan and J.A.B. Fortes, "Partitioning and Mapping Algorithms into fixed size systolic arrays", IEEE Trans. on Comp., C-35(1): 1–12, 1986.
D.I. Moldovan, C.I. Wu and J.A.B. Fortes, "Mapping an arbitrarily large QR algorithm into a fixed size VLSI array", Proc. of 1984 Int. Conf. on Parallel Processing, August 1984.
E.P. Papadopoulou, "VLSI structures and iterative analysis for large scale computation", Ph.D. Thesis, Clarkson University, 1986
E.P. Papadopoulou, T.S. Papatheodorou and Y.G. Saridakis, "Block AOR Iterative Schemes for Large-Scale Least-Squares Problems", to appear.
R.J. Plemmons, "Adjustment by least squares in geodesy using block iterative methods for sparse matrices", ARO Rept. 79-3, Proc. 1979 Army Num. Anal. Comp. Conf., El Paso, 1974.
J.R. Rice, RHRVEC workshop on very large least squares problems and supercomputers, CSD-TR 464, Computer Science Dept., Purdue University, Purdue, Indiana, 1983.
A.H. Sameh and R.P. Brent, "Solving Triangular Systems on a Parallel Computer", SIAM J. Number. Anal., Vol. 14, No. 6, pp. 1101–1113, Dec. 1977.
D.M. Young, "Iterative Solution of Large Linear Systems", Academic Press, New York, 1971.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papadopoulou, E.P., Papatheodorou, T.S. (1988). Least-squares iterative solution on a fixed-size VLSI architecture. In: Houstis, E.N., Papatheodorou, T.S., Polychronopoulos, C.D. (eds) Supercomputing. ICS 1987. Lecture Notes in Computer Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18991-2_53
Download citation
DOI: https://doi.org/10.1007/3-540-18991-2_53
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18991-6
Online ISBN: 978-3-540-38888-3
eBook Packages: Springer Book Archive