An Error-Free Transformation for Matrix Multiplication with Reproducible Algorithms and Divide and Conquer Methods

Katsuhisa Ozaki
2020 Journal of Physics, Conference Series  
This paper discusses accurate numerical algorithms for matrix multiplication. Matrix multiplication is a basic and important problem in numerical linear algebra. Numerical computations using floating-point arithmetic can be quickly performed on existing computers. However, the accumulation of rounding errors due to finite precision arithmetic is a critical problem. An error-free transformation for matrix multiplication is reviewed in this paper. Such a transformation is extremely useful for
more » ... mely useful for developing accurate numerical algorithms for matrix multiplication. One advantage of the transformation is that it exploits Basic Linear Algebra Subprograms (BLAS). We provide a rounding error analysis of reproducible algorithms for matrix multiplication based on the error-free transformation. In addition, we propose an errorfree transformation for matrix multiplication that can be utilized with the divide and conquer methods.
doi:10.1088/1742-6596/1490/1/012062 fatcat:gjzfhiqjbnhu3jygtqkxlvr4ce