Perturbation Bounds for Matrix Square Roots and Pythagorean Sums
By Fachbereich, Mathemutik, Universitiit, Marburg, Lahnberge. 2003
Perturbation estimates for the square root R := AlI2 and Pythagorean sum P := (1 + A’)‘/’ of complex matices are proved. We present bounds in the spectral norm for the cases that R and P are accretive, i.e. have positive definite Hermitian parts, with special attention to the case of a large condition of A. The results are based on bounds for the solution of the matrix Sylvester equation and for the separation of two matrices.
Subfields: Numerical Methods & Scientific Computing
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Citations in the corpus
- Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian (2019, positive): “2 of [51] guarantees that ∥A1/2 + −B1/2 + ∥ ≤ ∥A+ −B+∥ α .”