Complexities of special matrix multiplication problems

Takche, J.

Complexities of special matrix multiplication problems

Takche, J.

URI: http://hdl.handle.net/10725/7392

URL: https://www.sciencedirect.com/science/article/pii/0898122188901332

DOI: https://doi.org/10.1016/0898-1221(88)90133-2

Date: 2018-04-17

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Abstract:

This paper develops optimal algorithms to multiply an n × n symmetric tridiagonal matrix by: (i) an arbitrary n × m matrix using 2nm − m multiplications; (ii) a symmetric tridiagonal matrix using 6n − 7 multiplications; and (iii) a tridiagonal matrix using 7n −8 multiplications. Efficient algorithms are also developed to multiply a tridiagonal matrix by an arbitrary matrix, and to multiply two tridiagonal matrices.