In this paper we provide a sufficient and necessary condition for the eigenvalueand eigenvector of a general reducible matrix in a discrete-event system described by the“max”algebra,analyse the steady periodical per...In this paper we provide a sufficient and necessary condition for the eigenvalueand eigenvector of a general reducible matrix in a discrete-event system described by the“max”algebra,analyse the steady periodical performance of the system,and obtain ananalytic solution of the dynamic equation.We propose the conception of“order-d-(?)-block-periodical matrix”and obtain its sufficient and necessary condition and provide an algorithmof (?) matrix.展开更多
Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear...Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear element, based on box-splines, are taken as the first stage Khuh -λh/1Mh/1Uh. In this paper, the j-th stage neighboring-grid scheme is defined as Khuh λh/j Mh/j Uh = λh/j Mh/j Uh , where gh ：- Mh/j-1 Kh/1 and Mhuh is to be found as a better mass distribution over the j-th stage neighboring-grid G（/k）, and Kh/1 can be seen as an expansion of Kh on the j-th neighboring-grid with respect to the （j - 1）-th mass distribution Mh_l. It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even （2j ＋ 2）-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j ≤ 3.展开更多
1 Problem and algorithmMANY computing tasks arising from computational physics, chemistry and biology are relatedto solving so-called generalized eigen-decomposition problems. Consider the following general-ized eigen...1 Problem and algorithmMANY computing tasks arising from computational physics, chemistry and biology are relatedto solving so-called generalized eigen-decomposition problems. Consider the following general-ized eigen-decomposition problem:展开更多
文摘In this paper we provide a sufficient and necessary condition for the eigenvalueand eigenvector of a general reducible matrix in a discrete-event system described by the“max”algebra,analyse the steady periodical performance of the system,and obtain ananalytic solution of the dynamic equation.We propose the conception of“order-d-(?)-block-periodical matrix”and obtain its sufficient and necessary condition and provide an algorithmof (?) matrix.
基金supported by National Natural Science Foundation of China(Grant Nos.6097008961170075 and 91230109)
文摘Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear element, based on box-splines, are taken as the first stage Khuh -λh/1Mh/1Uh. In this paper, the j-th stage neighboring-grid scheme is defined as Khuh λh/j Mh/j Uh = λh/j Mh/j Uh , where gh ：- Mh/j-1 Kh/1 and Mhuh is to be found as a better mass distribution over the j-th stage neighboring-grid G（/k）, and Kh/1 can be seen as an expansion of Kh on the j-th neighboring-grid with respect to the （j - 1）-th mass distribution Mh_l. It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even （2j ＋ 2）-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j ≤ 3.
文摘1 Problem and algorithmMANY computing tasks arising from computational physics, chemistry and biology are relatedto solving so-called generalized eigen-decomposition problems. Consider the following general-ized eigen-decomposition problem:
