𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

✍ Scribed by Konstantin E. Avrachenkov; Moshe Haviv

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
208 KB
Volume
369
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices.

πŸ“œ SIMILAR VOLUMES

COMPARING THE PERTURBED EIGENSOLUTIONS O
COMPARING THE PERTURBED EIGENSOLUTIONS OF A GENERALIZED AND A STANDARD EIGENVALUE PROBLEM
✍ P.D. CHA; W. GU πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 132 KB

A frequently encountered scenario in structural dynamics is determining the changes in the eigensolution of a system after certain modi"cations are introduced. Clearly, if these modi"cations are substantial, then a new analysis and computational cycle are necessary in order to compute the new eigend

The inversion problem and applications o
The inversion problem and applications of the generalized radon transform
✍ Gregory Beylkin πŸ“‚ Article πŸ“… 1984 πŸ› John Wiley and Sons 🌐 English βš– 708 KB

We prove that under certain conditions the inversion problem for the generalized Radon transform reduces to solvinga Fredholm integral equation and we obtain the asymptoticexpansionof the symbolof the integral operator in this equation. We consider applications of the generalized Radon transform to