Showing papers on "Homotopy analysis method published in 1988"
TL;DR: In this article, a homotopy method for solving polynomial systems of equations is presented, which is linear with respect to the homogonality of the problem and only one auxiliary parameter is needed to regularize the problem.
Abstract: A new homotopy method for solving systems of polynomial equations is presented. The homotopy equation is extremely simple: It is linear with respect to the homotopy parameter and only one auxiliary parameter is needed to regularize the problem. Within some limits, an arbitrary starting problem can be chosen, as long as its solution set is known. No restrictions on the polynomial systems are made. A few numerical tests are reported which show the influence of the auxiliary parameter, resp. the starting problem, upon the computa- tional cost of the method.
47 citations
TL;DR: This note offers a simpler proof than Li and Sauer's of the existence of homotopy curves for eigenvalue problems of general matrices for linear algebraic eigen value problems on SIMD machines.
21 citations
TL;DR: There are homotopy algorithms for polynomial systems of equations that are globally convergent from an arbitrary starting point with probability one, are guaranteed to find all the solutions, and are robust, accurate, and reasonably efficient.
Abstract: Polynomial systems consist of n polynomial functions in n variables, with real or complex coefficients. Finding zeros of such systems is challenging because there may be a large number of solutions, and Newton-type methods can rarely be guaranteed to find the complete set of solutions. There are homotopy algorithms for polynomial systems of equations that are globally convergent from an arbitrary starting point with probability one, are guaranteed to find all the solutions, and are robust, accurate, and reasonably efficient. There is inherent parallelism at several levels in these algorithms. Several parallel homotopy algorithms with different granularities are studied on several different parallel machines, using actual industrial problems from chemical engineering and solid modeling.
9 citations
07 Jun 1988
TL;DR: In this article, the authors presented an efficient algorithm for solving bipolar transistor networks using two types of formulation techniques, namely, the topological formulation and the n-port formulation, in which the equation f(x)=0 is solved by a homotopy method.
Abstract: The authors present an efficient algorithm for solving bipolar transistor networks Two types of formulation techniques are used for deriving a network equation, ie, the topological formulation and the n-port formulation The equation f(x)=0 is solved by a homotopy method, in which a homotopy h(x,t)=f(x)-(1-t)f(x/sup 0/) is introduced and the solution curve of h(x,t)=0 is traced from an obvious solution (x/sup 0/,0) to the solution (x*,1) which is sought It is shown that the convergence of the algorithm is guaranteed by fairly mild conditions A rectangular subdivision and an upper bounding technique of linear programming are used for tracing the solution curve >
7 citations
5 citations
03 Aug 1988
TL;DR: In this paper, the authors present an approach for adaptive parametric spectrum modeling that is based on numerical continuation methods derived from homotopy theory, a branch of algebraic topology, applied to system identification using the linear finite-impulse-response filter structure.
Abstract: The authors present initial investigations into a novel approach for adaptive parametric spectrum modeling that is based on numerical continuation methods derived from homotopy theory, a branch of algebraic topology. This initial investigation focuses on homotopies applied to system identification using the linear finite-impulse-response filter structure, to illustrate the transition from homotopy theory to the adaptive filtering of time series. Homotopy-based continuation methods are globally convergent numerical procedures from which robust adaptive infinite-impulse-response algorithms may eventually be derived. Homotopy theory is reviewed, and the theoretical justification for its application to the adaptive filtering of time series is presented. The practical problems associated with the development of homotopy-based adaptive algorithms are discussed in detail. >
3 citations
TL;DR: While the algorithm is primarily of theoretical interest, preliminary computer experiments suggest orthant counts typically favorable to Lemke pivots on large problems.
3 citations
01 Feb 1988
1 citations
TL;DR: Both methods are effective for calculating multiple load flow solutions of ill-conditioned power system while the Newton homotopy method is more effective than the fixed point homotology method.
Abstract: The combination of fixed point homotopy method and simplicial subdivision method is called simply the fixed point homotopy method and that of Newton homotopy method and simplicial subdivision method is called simply the Newton homotopy method. Both methods are effective for calculating multiple load flow solutions of ill-conditioned power system while the Newton homotopy method is more effective than the fixed point homotopy method
Journal Article•
TL;DR: In this paper, a Backlund transformation that can be integrated with a linear homotopy operator is used to construct explicit solutions to initial value problems for linear balance equations, which are not balance equations.
01 Jan 1988
TL;DR: In this article, two models from population dynamics consisting of delay-Volterra patches connected by discrete diffusion are considered and homotopy techniques can be applied to derive sufficient conditions for the existence of a positive equilibrium globally asymptotically stable.
Abstract: We consider two models from population dynamics consisting of delay-Volterra patches connected by discrete diffusion and we show that the homotopy techniques can be applied to derive sufficient conditions for the existence of a positive equilibrium globally asymptotically stable.