## Error Analysis of Algorithms for Matrix Multiplication and
Triangular Decomposition using Winograd's Identity

4. R. P. Brent, Error analysis of algorithms for matrix multiplication and
triangular decomposition using Winograd's identity,
* Numerische Mathematik* 16 (1970), 145-156.
CR 12#21408,
MR 43#5702.
Abstract:
dvi (2K),
pdf (59K).

Paper:
pdf (925K).

## Abstract

The number of multiplications required for matrix multiplication,
for the triangular decomposition of a matrix with partial pivoting,
and for the Cholesky decomposition of a positive definite symmetric matrix,
can be roughly halved if Winograd's identity is used to compute the inner
products involved. Floating-point error bounds for these algorithms are shown
to be comparable to those for the normal methods provided that care is taken
with scaling.
## Comment

For the application of Winograd's identity to matrix multiplication,
and an error analysis of Strassen's matrix multiplication algorithm,
see Brent
[2].
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