Displaying similar documents to “Parallelism in numerical analysis”

The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)

Antonio J. Guirao, Olena Kozhushkina (2013)

Studia Mathematica

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We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).

Computing the numerical range of Krein space operators

Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)

Open Mathematics

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Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their...

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

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We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results...

Numerical analysis and systems theory

Stephen Campbell (2001)

International Journal of Applied Mathematics and Computer Science

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The area of numerical analysis interacts with the area of control and systems theory in a number of ways, some of which are widely recognized and some of which are not fully appreciated or understood. This paper will briefly discuss some of these areas of interaction and place the papers in this volume in context.