论文信息 - VLSI implementation of iterative methods for the solution of linear systems

VLSI implementation of iterative methods for the solution of linear systems

Abstract Area-time upper bounds for the iterative solution of linear systems and for the inversion of matrices in VLSI models are obtained and compared to the known upper bounds obtained by direct methods. Error analysis gives the number of iterations for which an acceptable error bound is obtained in the result. The use of the Jacobi method to solve partial differential equations is discussed.

[1] Franco P. Preparata,et al. Area-Time Optimal VLSI Networks for Multiplying Matrices , 1980, Inf. Process. Lett..

[2] James Hardy Wilkinson,et al. Rounding errors in algebraic processes , 1964, IFIP Congress.

[3] J. Gillis,et al. Matrix Iterative Analysis , 1961 .

[4] Franco P. Preparata,et al. A Mesh-Connected Area-Time Optimal VLSI Multiplier of Large Integers , 1983, IEEE Transactions on Computers.

[5] Charles E. Leiserson,et al. Area-Efficient Graph Layouts (for VLSI) , 1980, FOCS.

[6] Kurt Mehlhorn,et al. AT2-optimal VLSI integer division and integer square rooting , 1984, Integr..

[7] H. T. Kung,et al. Numerically Stable Solution of Dense Systems of Linear Equations Using Mesh-Connected Processors , 1984 .

[8] P.P.G. Kramer,et al. Systolic computation and VLSI , 1982 .

[9] H. Woźniakowski. Round-off error analysis of iterations for large linear systems , 1978 .

[10] F. Leighton. New lower bound techniques for VLSI , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).