TR-2004014: A Homotopic/Factorization Process for Toeplitz-like Matrices with Newton's/Conjugate Gradient Stages

We modify our earlier homotopic process for iterative inversion of Toeplitz and Toeplitz-like matrices to improve the choice of the initial approximate inverses at every homotopic step. This enables us to control the condition of the auxiliary matrices and to accelerate convergence substantially. The algorithm extends our older approach where the input matrix was factorized into the product of better conditioned factors, which are more readily invertible with the conjugate gradient algorithm. Now we study a similar factorization as a homotopic process and use the option of inverting all or some factors by applying Newton’s iteration where initial approximate inverses are readily available.