Complexities of special matrix multiplication problems

Complexity of Matrix Multiplication and Bilinear Problems

Algebraic complexity theory is the study of computation using algebraic models. One of the main achievements of this field has been the introduction of methods to prove lower bounds on the computational complexity, in algebraic models of computation, of concrete problems. Another major achievement has been the development of powerful techniques to construct fast algorithms for computational pro...

Quantum Complexity of Boolean Matrix Multiplication and Related Problems

Fast Algorithms with Preprocessing for Matrix-Vector Multiplication Problems

In this paper the problem of complexity o f m ultiplication of a matrix with a vector is studied for Toeplitz, Hankel, Vandermonde and Cauchy matrices and for matrices connected with them i.e. for transpose, inverse and transpose to inverse matrices. The proposed algorithms have complexities at most On log 2 n ops and in a number of cases improve the known estimates. In these algorithms, in a s...

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

Fast Matrix Multiplication

We give an overview of the history of fast algorithms for matrix multiplication. Along the way, we look at some other fundamental problems in algebraic complexity like polynomial evaluation. This exposition is self-contained. To make it accessible to a broad audience, we only assume a minimal mathematical background: basic linear algebra, familiarity with polynomials in several variables over r...