We will place certain parts of the theory of statistical efficiency into the author’s operator trigonometry (1967), thereby providing new geometrical understanding of statistical efficiency. Important earlier results of Bloomfield and Watson, Durbin and Kendall, Rao and Rao, will be so interpreted. For example, worse case relative least squares efficiency corresponds to and is achieved by the m...

The simulated models and requirements of engineering programs like computational fluids dynamics and structural mechanics grow more rapidly than single processor performance. Automatic parallelisation seem to be the obvious approach for huge and historic packages like PERMAS. In this paper we evaluate how preparatory steps on the big input matrices can improve the performance of the parallelisa...

Advances in their technologies have positioned FPGAs and embedded processors to compete with digital signal processors (DSPs). In this paper, we evaluate the performance in terms of both latency and energy-efficiency of FPGAs, embedded processors, and DSPs in multiplying two matrices. As specific examples, we have chosen a representative of each type of device. Our results show that the FPGAs c...

The effect of single and double-layer anti-reflective coatings on efficiency enhancement of silicon solar cells was investigated. The reflectance of different anti-reflection structures were calculated using the transfer matrix method and then to predict the performance of solar cells coated by these structures, the weighted average reflectance curves were used as an input of a PC1D simulation....

Cross-efficiency evaluation is an effective way of ranking decision making units (DMUs) in data envelopment analysis (DEA). Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficienc...

Introduction: Data envelopment analysis (DEA) is a data-oriented method for measuring and benchmarking the relative efficiency of peer decision making units (DMUs) with multiple inputs and multiple outputs. DEA was initiated in 1978 when Charnes, Cooper and Rhodes (CCR) demonstrated how to change a fractional linear measure of efficiency into a linear programming format. This non-parametric app...

In this paper, we present a numerical algorithm for solving matrix equations $(A otimes B)X = F$  by extending the well-known Gaussian elimination for $Ax = b$. The proposed algorithm has a high computational efficiency. Two numerical examples are provided to show the effectiveness of the proposed algorithm.

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.