A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlat...A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.展开更多
In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. ...In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.展开更多
基金supported by the National Natural Science Foundation for Excellent Young Scholars(Grant 51222502)the National Natural Science Foundation of China(Grant 11172096)the Funds for State Key Laboratory of Construction Machinery(SKLCM2014-1)
文摘A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
基金Supported by National Natural Science Foundation of China(11201370)the Science and Technology Program of Shaanxi Province of China(2013JM1017,2014JM1007,2014KJXX-61)the Natural Science Foundation of the Education Department of Shaanxi Province of China(2013JK0558)
文摘In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.
