In this paper we unveil some performance and energy efficiency frontiers for sparse computations on GPU-based supercomputers. We compare the resource efficiency of different sparse matrix–vector products (SpMV) taken from libraries such as cuSPARSE and MAGMA for GPU and Intel’s MKL for multicore CPUs, and develop a GPU sparse matrix–matrix product (SpMM) implementation that handles the simultan...

For a random set $\mathcal{S} \subset U(d)$ of quantum gates we provide bounds on the probability that $\mathcal{S}$ forms $\delta$-approximate $t$-design. In particular have found for drawn from an exact $t$-design it satisfies inequality $\mathbb{P}\left(\delta \geq x \right)\leq 2D_t \, \frac{e^{-|\mathcal{S}| \mathrm{arctanh}(x)}}{(1-x^2)^{|\mathcal{S}|/2}} = O\left( \left( \frac{e^{-x^2}}{...

With the rapid growth of online text information and user accesses, query-processing efficiency has become the major bottleneck of information retrieval (IR) systems. This paper proposes two new full-text indexing models to improve query-processing efficiency of IR systems. By using directed graph to represent text string, the adjacency matrix of text string is introduced. Two approaches are pr...

The straightforward implementation of interval matrix product suffers from poor efficiency, far from the performances of highly optimized floating-point implementations. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix products for performance issues without sacrificing the quality of the result. We show that, compared to the straightforward imp...

the present paper offers a meso-scale numerical model to investigate the effects of random distribution of aggregate particles and steel fibers on the elastic modulus of steel fiber reinforced concrete (sfrc). meso-scale model distinctively models coarse aggregate, cementitious mortar, and interfacial transition zone (itz) between aggregate, mortar, and steel fibers with their respective materi...

Recursion’s removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as fast matrix multiplication algorithms. In this article, a general method of breaking recursions in fast matrix multiplication algorithms is introduced, which is generalized from recursions removal of a specific fast matrix multiplication algorithm of Winograd.

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...