This dissertation introduces the notion of a dynamic inverse of a nonlinear map. The
dynamic inverse is used in the construction of nonlinear dynamical system, called a dynamic …

We show how to obtain polar decomposition as well as inversion of fixed and time-varying
matrices using a class of nonlinear continuous-time dynamical systems. First we construct a …

A new class of homotopy continuation methods is developed suitable for globalizing quasi-
Newton methods for large sparse nonlinear systems of equations. The new continuation …

We consider the problem of estimating the time-varying root of a time-dependent nonlinear
map. We introduce a" dynamic inverse" of a map, another generally time-dependent map …

We present a controller for a class of robotics manipulators which provides exponential
convergence to a desired end-effector trajectory using gains specified in joint-space. This is …

A new monolithic homotopy continuation algorithm is presented. The algorithm can be used
to globalize Newton's method for solving large sparse systems of nonlinear equations. The …

New homotopy continuation algorithms are developed and applied to a parallel implicit finite-
difference Newton-Krylov-Schur external aerodynamic flow solver for the compressible …

A matrix-free monolithic homotopy continuation algorithm is developed which allows for
approximate numerical solutions to nonlinear systems of equations without the need to solve …