Skip to main content

Stability of fast algorithms for matrix multiplication


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.

This is a preview of subscription content, access via your institution.


  1. 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. 2.

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

    Google Scholar 

  3. 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. 4.

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

  5. 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. 6.

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

    Google Scholar 

  7. 7.

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

    Google Scholar 

  8. 8.

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

    Article  Google Scholar 

  9. 9.

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

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

Subject Classifications

  • AMS (MOS): 15A63
  • CR: 5.14