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Related with accuracy, computational complexity and so on, quality of computing for the so-called homotopy method has been discussed recently. In this paper, we shall propose an estimation method with interval analysis of region in which unique solution path of the homotopy equation is guaranteed to exist, when it is applied to a certain class of uniquely solvable nonlinear equations. By the estimation, we can estimate the region a posteriori, and estimate a priori an upper bound of the region.
Kiyotaka YAMAMURA Tooru SEKIGUCHI
Tracing solution curves of nonlinear equations is an important problem in circuit simulation. In this paper, simple techniques are proposed for improving the computational efficiency of the spherical method, which is a method for tracing solution curves. These techniques are very effective in circuit simulation where solution curves often turn very rapidly. Moreover, they can be easily performed with little computational effort.
A simple technique is proposed for improving the convergence of Newton's method in the spherical algorithms, which are metheods for tracing solution curves. A numerical example is given in order to show the effectiveness of the proposed technique.