Robert, Yves Solving dense linear systems on systolic architectures. (English) Zbl 0763.65015 Algorithms and parallel VLSI architectures. Vol. A: Tutorials, Lect. Tutorials Int. Workshop, Pont-à-Mousson/Fr. 1990, 363-401 (1991). [For the entire collection see Zbl 0746.00066.]The paper gives a survey about the systolic arrays for the solution of dense linear systems using Gaussian elimination and Givens factorization. Implementations on two-dimensional arrays which include on-the-fly solution of the triangular system after the factorization are discussed. Then a space-time minimal systolic array for the Gaussian elimination is derived. Finally, efficient systolic algorithms for matrices over finite fields are presented. Reviewer: P.Y.Yalamov (Russe) MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 65Y10 Numerical algorithms for specific classes of architectures 68Q80 Cellular automata (computational aspects) 15B33 Matrices over special rings (quaternions, finite fields, etc.) Keywords:systolic arrays; linear systems; Gaussian elimination; Givens factorization; systolic algorithms; finite fields Citations:Zbl 0746.00066 PDFBibTeX XMLCite \textit{Y. Robert}, in: Algorithms and parallel VLSI architectures. Vol. A: Tutorials. Lectures and tutorials presented at the international workshop, Pont-à-Mousson, France, June 10-16, 1990. Amsterdam: Elsevier. 363--401 (1991; Zbl 0763.65015)