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Relations between exact and approximate bilinear algorithms. Applications. (English) Zbl 0459.65028


MSC:

65F30 Other matrix algorithms (MSC2010)
15A63 Quadratic and bilinear forms, inner products
68Q25 Analysis of algorithms and problem complexity
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References:

[1] Bini D.,Border Rank of a p{\(\times\)}q{\(\times\)}2 Tensor and the Optimal Approximation of a Pair of Bilinear Forms. Lecture Notes on Computer Science85. Automata Languages and Programming (1980). · Zbl 0445.68028
[2] Bini, D., Capovani M., Lotti G., Romani F., 0(n 2.7799)Complexity for n{\(\times\)}n Approximate Matrix Multiplication. Information Processing Letters8 n0 5, (June 1979), 234–235. · Zbl 0395.68048 · doi:10.1016/0020-0190(79)90113-3
[3] Bini D., Lotti G., Romani F.,Approximate Solution for the Bilinear Form Computational Problem. SIAM J. Comp. (to appear). · Zbl 0446.68035
[4] Egervary E.,On Hypermatrices whose Blocks are Commutable in Pairs and their Application in Lattice-Dynamics. Acta Sci. Math. (Szeged),15, (1954), 211–222. · Zbl 0056.25103
[5] Isaacson E., Keller H. B.,Analysis of Numerical Methods. Jhon Wiley and Sons, New York 1966. · Zbl 0168.13101
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[7] Pan V., Ya., Winograd S.,Personal Communication.
[8] Paterson M. S.,Complexity of Matrix Algorithms in Foundations of Computer Science. Mathematical Centre Tracts,63, Amsterdam (1975).
[9] Pease M. C.,Methods of Matrix Algebra, Academic Press New York, (1965). · Zbl 0145.03701
[10] Schonhage A.,Total and Partial Matrix Multiplication. Tech. Rep., Mathematisches Institute of Universitat. Tubingen, (1980).
[11] Strassen V.,Gaussian Elimination is not Optimal. Numer. Math.13, (1969), 354–356. · Zbl 0185.40101 · doi:10.1007/BF02165411
[12] Strassen V.,Vermeidung von Divisionen, J. Reine Angew. Math.246, (1975), 184–202.
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