Displaying similar documents to “The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations”

Determination of the diffusion operator on an interval

Ibrahim M. Nabiev (2014)

Colloquium Mathematicae

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The inverse problem of spectral analysis for the diffusion operator with quasiperiodic boundary conditions is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solvability of the inverse problem are obtained.

Generalized inverses in C*-algebras II

Robin Harte, Mostafa Mbekhta (1993)

Studia Mathematica

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Commutativity and continuity conditions for the Moore-Penrose inverse and the "conorm" are established in a C*-algebra; moreover, spectral permanence and B*-properties for the conorm are proved.

Identification of a wave equation generated by a string

Amin Boumenir (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.

The Direct and Inverse Spectral Problems for some Banded Matrices

Zagorodnyuk, S. M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 15A29. In this paper we introduced a notion of the generalized spectral function for a matrix J = (gk,l)k,l = 0 Ґ, gk,l О C, such that gk,l = 0, if |k-l | > N; gk,k+N = 1, and gk,k-N № 0. Here N is a fixed positive integer. The direct and inverse spectral problems for such matrices are stated and solved. An integral representation for the generalized spectral function is obtained.

A numerical radius inequality involving the generalized Aluthge transform

Amer Abu Omar, Fuad Kittaneh (2013)

Studia Mathematica

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A spectral radius inequality is given. An application of this inequality to prove a numerical radius inequality that involves the generalized Aluthge transform is also provided. Our results improve earlier results by Kittaneh and Yamazaki.

A simple spectral algorithm for recovering planted partitions

Sam Cole, Shmuel Friedland, Lev Reyzin (2017)

Special Matrices

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In this paper, we consider the planted partition model, in which n = ks vertices of a random graph are partitioned into k “clusters,” each of size s. Edges between vertices in the same cluster and different clusters are included with constant probability p and q, respectively (where 0 ≤ q < p ≤ 1). We give an efficient algorithm that, with high probability, recovers the clusters as long as the cluster sizes are are least (√n). Informally, our algorithm constructs the projection operator...

Notes on some spectral radius and numerical radius inequalities

Amer Abu-Omar, Fuad Kittaneh (2015)

Studia Mathematica

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We prove numerical radius inequalities for products, commutators, anticommutators, and sums of Hilbert space operators. A spectral radius inequality for sums of commuting operators is also given. Our results improve earlier well-known results.

A Sturm-Liouville problem with spectral and large parameters in boundary conditions and the associated Cauchy problem

Jamel Ben Amara (2011)

Colloquium Mathematicae

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We study a Sturm-Liouville problem containing a spectral parameter in the boundary conditions. We associate to this problem a self-adjoint operator in a Pontryagin space Π₁. Using this operator-theoretic formulation and analytic methods, we study the asymptotic behavior of the eigenvalues under the variation of a large physical parameter in the boundary conditions. The spectral analysis is applied to investigate the well-posedness and stability of the wave equation of a string. ...