Acute perturbation bounds of weighted Moore–Penrose inverse

Ma, Haifeng

doi:10.1080/00207160.2017.1294689

Cited by 11 publications

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second formulation is the focus of this article and considers a matrix A and two matrices, S and T, which define inner products on the range and column space of A, respectively. This formulation, which we refer to as the (S, T)-GSVD, arises naturally in a variety of applications including: singular value expansions of compact integral operator (such as Fredholm integral equation of the first kind) Reference 4, section 2.4, weighted least squares, 8 weighted inverse problems, 3 uncertainty quantification, 9 inverse problems, 10 model reduction, 11 and HDSA. 12 In many of the aforementioned applications of the (S, T)-GSVD, the matrix A arises from discretizing a differential (or integral) equation while S and T define inner products in the discretized function space(s).…”

Section: Introductionmentioning

confidence: 99%

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

Saibaba

Hart

Waanders

2021

Numerical Linear Algebra App

View full text Add to dashboard Cite

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

show abstract

Section: Introductionmentioning

confidence: 99%

Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

Saibaba

Hart

Waanders

2021

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…Recently, we extend the acute perturbation from the Moore-Penrose inverse to the weighted Moore-Penrose inverse [17].…”

mentioning

confidence: 99%

“…Motivated by the acute perturbation of the Moore-Penrose inverse [21,26], weighted Moore-Penrose inverse [17] and the group inverse [31], we present the acute perturbation for the Drazin inverse with respect to the spectral radius instead of the spectral norm, which extends the recent results on the group inverse by Wei in [31]. Definition 2.1.…”

mentioning

confidence: 99%

Further results on the perturbation estimations for the Drazin inverse

Ma¹,

Gao²

2018

Numerical Algebra, Control &Amp; Optimization

Self Cite

View full text Add to dashboard Cite

For n × n complex singular matrix A with ind(A) = k > 1, let A D be the Drazin inverse of A. If a matrix B = A + E with ind(B) = 1 is said to be an acute perturbation of A, if E is small and the spectral radius ofThe acute perturbation coincides with the stable perturbation of the group inverse, if the matrix B satisfies geometrical condition:which introduced by Vélez-Cerrada, Robles, and Castro-González, (Error bounds for the perturbation of the Drazin inverse under some geometrical conditions, Appl. Math. Comput., 215 (2009), 2154-2161).Furthermore, two examples are provided to illustrate the acute perturbation of the Drazin inverse. We prove the correctness of the conjecture in a special case of ind(B) = 1 by Wei ( Acute perturbation of the group inverse, Linear Algebra Appl., 534 (2017), 135-157).

show abstract