in this paper operational matrix of bernstein polynomials (bps) is used to solve bratu equation. this nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. by using operational matrix of fractional integration...

A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve upper bounds on the exponent of matrix multiplication yielded by group-theoretic full matrix multiplication. The group theory behind our partial matrix multipli...

In this paper, we present our work on developing a new matrix format and a new sparse matrix-vector multiplication algorithm. The matrix format is HEC, which is a hybrid format. This matrix format is efficient for sparse matrix-vector multiplication and is friendly to preconditioner. Numerical experiments show that our sparse matrix-vector multiplication algorithm is efficient on

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...

These notes are based on a lecture given at the Toronto Student Seminar on February 2, 2012. The material is taken mostly from the book Algebraic Complexity Theory [ACT] and the lecture notes by Bläser and Bendun [Blä]. Starred sections are the ones I didn't have time to cover. This lecture discusses the problem of multiplying two square matrices. We will be working in the algebraic complexity ...

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

The Strassen algorithm and Winograd’s variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate singleas well as double-precision matrix multiplication by using these algorithms, no research to date has been undertaken to accelerate multiple precision matrix multiplication. In this pa...