Homotopy continuation method for the numerical solutions of generalised symmetric eigenvalue problems

Numerical Polynomial Homotopy Continuation Method to Locate All The Power Flow Solutions

The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here we introduce a novel form of homotopy continuation method called the numeric...

The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems

A new algorithm is developed which computes a specified number of eigenvalues in any part of the spectrum of a generalized symmetric matrix eigenvalue problem. It uses a linear system routine (factorization and solution) as a tool for applying the Lanczos algorithm to a shifted and inverted problem. The algorithm determines a sequence of shifts and checks that all eigenvalues get computed in th...

Rational Homotopy Groups of Generalised Symmetric Spaces

We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In particular, this gives explicit formulas for the rational homotopy groups of all classical compact symmetric spaces.

Oettli The Homotopy Method Applied to Eigenvalue Problems

Homotopy Continuation Methods for Nonlinear Complementarity Problems

A complementarity problem with a continuous mapping f from R n into itself can be written as the system of equations F(x, y ) = 0 and ( x , y ) > 0. Here F is the mapping from R ~ " into itself defined by F(x, y) = ( x l y ,, x 2 y Z , . . . , x , ~ y e , y f f x ) ) . Under the assumption that the mapping f is a P,,-function, we study various aspects of homotopy continuation methods that trace...