Fast parallel algorithms for QR and triangular factorization
SIAM Journal on Scientific and Statistical Computing
An improved Newton interaction for the generalized inverse of a Matrix, with applications
SIAM Journal on Scientific and Statistical Computing
Decreasing the displacement rank of a matrix
SIAM Journal on Matrix Analysis and Applications
Parallel solution of Toeplitzlike linear systems
Journal of Complexity
Displacement structure: theory and applications
SIAM Review
Newton's iteration for structured matrices
Fast reliable algorithms for matrices with structure
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Inversion of Displacement Operators
SIAM Journal on Matrix Analysis and Applications
A Homotopic Residual Correction Process
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Iterative inversion of structured matrices
Theoretical Computer Science - Algebraic and numerical algorithm
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We modify our earlier homotopic (continuation) process for iterative matrix inversion to improve the choice of the initial approximate inverse at every homotopic step. This enables us to control the condition of the auxiliary matrices and to accelerate the convergence of the iteration. The algorithm also extends our earlier approach where we factorized the input matrix into the product of better conditioned factors. We accelerate our new algorithm in the case of a Toeplitz-like input, comment on the extensions to the computations with other structured matrices such as Cauchy-Pick and banded matrices, and propose new techniques for the compression of the displacement of Hermitian matrices.