In this paper,a generalized model of the reactive distillation processes was developed via rate-based approach. The homotopy-continuation method was employed to solve the complicated nonlinear model equations efficien...In this paper,a generalized model of the reactive distillation processes was developed via rate-based approach. The homotopy-continuation method was employed to solve the complicated nonlinear model equations efficiently. The simulation on the reactive distillation processes was carried out with the profiles of stage temperature,composition and flow rate for both vapor and liquid phases obtained. Based on careful analysis of the simulation results, the pitfalls in experimental design were detected. Finally, a software package for the simulation of reactive distillation processes was developed.展开更多
Motivated by the idea of Shen, et al.'s work, which proposed a hybrid procedure for real root isolation of polynomial equations based on homotopy continuation methods and interval analysis,this paper presents a hy...Motivated by the idea of Shen, et al.'s work, which proposed a hybrid procedure for real root isolation of polynomial equations based on homotopy continuation methods and interval analysis,this paper presents a hybrid procedure to compute sample points on each connected component of a real algebraic set by combining a special homotopy method and interval analysis with a better estimate on initial intervals. For a real algebraic set given by a polynomial system, the new method ?rst constructs a square polynomial system which represents the sample points, and then solve this system by a special homotopy continuation method introduced recently by Wang, et al.(2017). For each root returned by the homotopy continuation method, which is a complex approximation of some(complex/real) root of the polynomial system, interval analysis is used to verify whether it is an approximation of a real root and ?nally get real points on the given real algebraic set. A new estimate on initial intervals is presented which helps compute smaller initial intervals before performing interval iteration and thus saves computation. Experiments show that the new method works pretty well on tested examples.展开更多
Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular p...Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular points are ordinary. The numerical procedures rely on computing numerical solutions of polynomial systems by homotopy continuation method and a reliable method that calculates multiple roots of the univariate polynomials accurately using standard machine precision. It is completely different from the traditional symbolic computation and provides singular points and their related properties of some plane algebraic curves that the symbolic software Maple cannot work out. Without using multiprecision arithmetic, extensive numerical experiments show that our numerical procedures are accurate, efficient and robust, even if the coefficients of plane algebraic curves are inexact.展开更多
A homotopy continuation adaptive HR filtering algorithm is proposed in this paper.The novel algorithm introduces the homotopy continuation method into the adaptive filtering soas to provide a high stability for adapti...A homotopy continuation adaptive HR filtering algorithm is proposed in this paper.The novel algorithm introduces the homotopy continuation method into the adaptive filtering soas to provide a high stability for adaptive HR filter without any forms of stability monitoringattached.展开更多
The aim of this paper is to study numerical realization of the conditions of Max Nother＇s residual intersection theorem. The numerical realization relies on obtaining the inter- section of two algebraic curves by hom...The aim of this paper is to study numerical realization of the conditions of Max Nother＇s residual intersection theorem. The numerical realization relies on obtaining the inter- section of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determin- ing the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time.展开更多
基金Supported by the State Key Project of the National Natural Science Foundation of China (No.2929054)
文摘In this paper,a generalized model of the reactive distillation processes was developed via rate-based approach. The homotopy-continuation method was employed to solve the complicated nonlinear model equations efficiently. The simulation on the reactive distillation processes was carried out with the profiles of stage temperature,composition and flow rate for both vapor and liquid phases obtained. Based on careful analysis of the simulation results, the pitfalls in experimental design were detected. Finally, a software package for the simulation of reactive distillation processes was developed.
基金supported by the National Natural Science Foundation of China under Grant Nos.61732001 and 61532019
文摘Motivated by the idea of Shen, et al.'s work, which proposed a hybrid procedure for real root isolation of polynomial equations based on homotopy continuation methods and interval analysis,this paper presents a hybrid procedure to compute sample points on each connected component of a real algebraic set by combining a special homotopy method and interval analysis with a better estimate on initial intervals. For a real algebraic set given by a polynomial system, the new method ?rst constructs a square polynomial system which represents the sample points, and then solve this system by a special homotopy continuation method introduced recently by Wang, et al.(2017). For each root returned by the homotopy continuation method, which is a complex approximation of some(complex/real) root of the polynomial system, interval analysis is used to verify whether it is an approximation of a real root and ?nally get real points on the given real algebraic set. A new estimate on initial intervals is presented which helps compute smaller initial intervals before performing interval iteration and thus saves computation. Experiments show that the new method works pretty well on tested examples.
基金The NSF (61033012,10801023,11171052,10771028) of China
文摘Given an irreducible plane algebraic curve of degree d 〉 3, we compute its numerical singular points, determine their multiplicities, and count the number of distinct tangents at each to decide whether the singular points are ordinary. The numerical procedures rely on computing numerical solutions of polynomial systems by homotopy continuation method and a reliable method that calculates multiple roots of the univariate polynomials accurately using standard machine precision. It is completely different from the traditional symbolic computation and provides singular points and their related properties of some plane algebraic curves that the symbolic software Maple cannot work out. Without using multiprecision arithmetic, extensive numerical experiments show that our numerical procedures are accurate, efficient and robust, even if the coefficients of plane algebraic curves are inexact.
文摘A homotopy continuation adaptive HR filtering algorithm is proposed in this paper.The novel algorithm introduces the homotopy continuation method into the adaptive filtering soas to provide a high stability for adaptive HR filter without any forms of stability monitoringattached.
基金Supported by the National Natural Science Foundation of China(61432003,61033012,11171052)
文摘The aim of this paper is to study numerical realization of the conditions of Max Nother＇s residual intersection theorem. The numerical realization relies on obtaining the inter- section of two algebraic curves by homotopy continuation method, computing the approximate places of an algebraic curve, getting the exact orders of a polynomial at the places, and determin- ing the multiplicity and character of a point of an algebraic curve. The numerical experiments show that our method is accurate, effective and robust without using multiprecision arithmetic, even if the coefficients of algebraic curves are inexact. We also conclude that the computational complexity of the numerical realization is polynomial time.
