LINEAR AND NONLINEAR DECONVOLUTION PROBLEMS (OPTIMIZATION)
OLKIN, JULIA ANN
Doctor of Philosophy
This dissertation considers computational methods for solving linear and nonlinear least squares problems arising from deconvolution applications. For the linear problems we propose a new preconditioner to speed up the conjugate gradient algorithm. This preconditioner is based on Cybenko's QR factorization of a circulant matrix. Several cases are presented in which our method reduces the amount of computation. The preconditioner is applied to the linear subproblems which arise from the linearization of the nonlinear problems. We investigate several algorithms which take advantage of the inherent Toeplitz structure. The scale degeneracy present in our nonlinear problems is also remedied.