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Stability of fast algorithms for matrix multiplication

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Non commutative fast algorithms to compute 2×2 matrix product are classified with regard to stability. An analysis of the rounding error propagation is presented for then×n matrix multiplication algorithms obtained by recursive partitioning.

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  1. Bank, R.E., Rose, D.J.: AnO(n2) method for solving constant coefficient boundary value problems in two dimensions. SIAM J. Numer. Anal.12, 529–540 (1975)

    Article  Google Scholar 

  2. Borodin, A., Munro, I.: Computational complexity of algebraic and numeric problems. New York: 1975 Elsevier

    Google Scholar 

  3. Brent, R.P.: Error analysis of algorithms for matrix multiplication and triangular decomposition using Winograd's identity. Numer. Math.16, 145–156 (1970)

    Google Scholar 

  4. Brent, R.P.: Algorithms for matrix multiplication. Report STAN-CS-70-157, Stanford University (1970)

  5. Brockett, R.W., Dobkin, D.: On the optimal evaluation of a set of bilinear forms. Linear Algebra and Appl.19, 207–235 (1978)

    Article  Google Scholar 

  6. Forsythe, G., Moler, C.: Computer solution of linear algebraic systems. Englewood Cliffs, N.J.: Prentice Hall (1967)

    Google Scholar 

  7. Miller, W.: Remark on the complexity of roundoff analysis. Computing12, 149–161 (1974)

    Google Scholar 

  8. Miller, W.: Computational complexity and numerical stability. SIAM J. Comput.4, 97–107 (1975)

    Article  Google Scholar 

  9. Strassen, V.: Gaussian elimination is not optimal. Numer. Math.13, 354–356 (1969)

    Google Scholar 

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Bini, D., Lotti, G. Stability of fast algorithms for matrix multiplication. Numer. Math. 36, 63–72 (1980).

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