Showing papers on "Homotopy analysis method published in 1982"

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

Abstract: A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that they provide a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.

On the computational complexity of piecewise-linear homotopy algorithms

Abstract: We show that piecewise-linear homotopy algorithms may take a number of steps that grows exponentially with the dimension when solving a system of linear equations whose solution lies close to the starting point. Our examples are based on an example of Murty exhibiting exponential growth for Lemke's algorithm for the linear complementarity problem.

An introduction to piecewise-linear homotopy algorithms for solving systems of equations

Abstract: We describe a class of algorithms known as piecewise-linear homotopy methods for solving certain (generalized) zero-finding problems. The global and local convergence properties of these algorithms are discussed. We also outline recent techniques that have been proposed to improve the efficiency of the methods.