Flexible Krylov Methods for Edge Enhancement in Imaging

Autor: Silvia Gazzola, Sebastian James Scott, Alastair Spence

Publikováno v: Journal of Imaging, Vol 7, Iss 10, p 216 (2021)

Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-s

Externí odkaz: https://doaj.org/article/4b655259e0f64947a173d7fae97f5d02

Calculating the $H_{\infty}$-norm Using the Implicit Determinant Method

Autor: Alastair Spence, Melina A. Freitag, Paul Van Dooren

Publikováno v: Freitag, M A, Spence, A & Van Dooren, P 2014, ' Calculating the $H_{\infty}$-norm Using the Implicit Determinant Method ', SIAM Journal On Matrix Analysis and Applications (SIMAX), vol. 35, no. 2, pp. 619-635 . https://doi.org/10.1137/130933228

We propose a fast algorithm to calculate the $H_{\infty}$-norm of a transfer matrix. The method builds on a well-known relationship between singular values of the transfer function and pure imaginary eigenvalues of a certain Hamiltonian matrix. Using

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5369578039058c1cefd9cb195fae28f
https://doi.org/10.1137/130933228

The calculation of the distance to a nearby defective matrix

Autor: Alastair Spence, Melina A. Freitag, Richard O. Akinola

Publikováno v: Numerical Linear Algebra with Applications. 21:403-414

SUMMARY The distance of a matrix to a nearby defective matrix is an important classical problem in numerical linear algebra, as it determines how sensitive or ill-conditioned an eigenvalue decomposition of a matrix is. The concept has been discussed

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3b2c8f6bbf10bdc165dfd86b879c9a78
https://doi.org/10.1002/nla.1888

Convergence of inexact inverse iteration with application to preconditioned iterative solves

Autor: Melina A. Freitag, Alastair Spence

Publikováno v: Freitag, MA & Spence, A 2007, ' Convergence of inexact inverse iteration with application to preconditioned iterative solves ', BIT Numerical Mathematics, vol. 47, no. 1, pp. 27-44 . https://doi.org/10.1007/s10543-006-0100-1

In this paper we study inexact inverse iteration for solving the generalised eigenvalue problem A x=λM x. We show that inexact inverse iteration is a modified Newton method and hence obtain convergence rates for various versions of inexact inverse i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::667a4d5e21f17fe48db4e5e4fca7993a
https://doi.org/10.1007/s10543-006-0100-1

Analysis of Box Schemes for Reactive Flow Problems

Autor: K. W. Morton, Sarah L. Mitchell, Alastair Spence

Publikováno v: Mitchell, SL, Morton, KW & Spence, A 2006, ' Analysis of box schemes for reactive flow problems ', SIAM Journal on Scientific Computing, vol. 27, no. 4, pp. 1202-1225 . https://doi.org/10.1137/030601910

Key properties of the box scheme are shown to be advantageous for reactive flow problems. Unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the “reduced speed

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::caa0863804e1c10dacd9a283f80aafdb
https://doi.org/10.1137/030601910