Numerical bounds on the Crouzeix ratio for a class of matrices

Autor: Michel, Crouzeix, Anne, Greenbaum, Kenan, Li

We provide numerical bounds on the Crouzeix ratiofor KLS matrices $A$ which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all polynomials $p$ of the spectral norm of $p(A)$ dividedby the maximum a

Externí odkaz: http://arxiv.org/abs/2311.13890

The Numerical Range is a $(1+\sqrt{2})$-Spectral Set

Autor: Cesar Palencia, Michel Crouzeix

Publikováno v: SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (2), pp.649-655. 〈10.1137/17M1116672〉
SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2017, 38 (2), pp.649-655. ⟨10.1137/17M1116672⟩
SIAM Journal on Matrix Analysis and Applications, 2017, 38 (2), pp.649-655. ⟨10.1137/17M1116672⟩

8 pages; International audience; It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the c

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4050a7dd140717764a0c292b60336edb
https://doi.org/10.1137/17m1116672

The inf-sup constant for the divergence on corner domains

Autor: Martin Costabel, Michel Crouzeix, Yvon Lafranche, Monique Dauge

Publikováno v: Numerical Methods for Partial Differential Equations. 31:439-458

The inf-sup constant for the divergence, or LBB constant, is related to the Cosserat spectrum. It has been known for a long time that on non-smooth domains the Cosserat operator has a non-trivial essential spectrum, which can be used to bound the LBB

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::90d001d2a3814f23f02f13a03814c083
https://doi.org/10.1002/num.21916

From granules to bulk superconductors using Richardson-Gaudin equations

Autor: Michel Crouzeix, Monique Combescot

Publikováno v: European Physical Journal B: Condensed Matter and Complex Systems
European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2016, 89 (7), 6 p. 〈10.1140/epjb/e2016-70029-3〉
The European Physical Journal B: Condensed Matter and Complex Systems
The European Physical Journal B: Condensed Matter and Complex Systems, 2016, 89 (7), 6 p. ⟨10.1140/epjb/e2016-70029-3⟩
The European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2016, 89 (7), 6 p. ⟨10.1140/epjb/e2016-70029-3⟩

paper n° 164; International audience; We provide a compact expression of the ground-state energy of N-Cooper pairs valid from small to large sample volumes, as checked by numerically solving Richardson-Gaudin equations which give the exact eigenstat

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9577abaa39e0258c20d1536268fa2f2e
https://hal.archives-ouvertes.fr/hal-01377509

Bounds for Analytical Functions of Matrices

Autor: Michel Crouzeix

Publikováno v: Integral Equations and Operator Theory. 48:461-477

If f is an analytic function bounded on a convex domain of the complex plane and A a square matrix whose spectrum is included in this domain, the function f(A) is well defined. In this paper we study bounds for ||f(A)|| uniform with respect to the fu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::52679c07cc281dbcf564a8c609df1e74
https://doi.org/10.1007/s00020-002-1188-6