Introduction to Large Truncated Toeplitz Matrices

Böttcher, Albrecht; Silbermann, Bernd

doi:10.1007/978-1-4612-1426-7

Cited by 575 publications

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“…In fact we could use results on block Toeplitz matrices (see [2] and [7]) and we will discuss that point at the end of this article.…”

Section: The Resultsmentioning

confidence: 99%

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Szegö Type Results Relative to a Sequence of Model Spaces

Barusseau

2011

Complex Anal. Oper. Theory

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“…In fact we could use results on block Toeplitz matrices (see [2] and [7]) and we will discuss that point at the end of this article.…”

Section: The Resultsmentioning

confidence: 99%

“…We can find demonstrations in the continuous case using the operator theory and the C * -algebras in [2]. Let us recall this fundamental theorem : Theorem 2.…”

Section: A N Is Said To Be Distributed As F In the Sense Of The Singumentioning

confidence: 98%

Szegö Type Results Relative to a Sequence of Model Spaces

Barusseau

2011

Complex Anal. Oper. Theory

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“…We briefly recall some of the basics from the Laurent and Toeplitz operator theory from Böttcher & Silbermann (1999). Given a Laurent operator A L on l 2 (Z) …”

Section: (D) Tests On Laurent and Toeplitz Matricesmentioning

confidence: 99%

Infinite-dimensional numerical linear algebra: theory and applications

Hansen

2010

Proc. R. Soc. A.

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“…We apply the theory of Toeplitz matrices [1] to prove that H −1 d H l 2 = 1 for the n 1 = ∞ case. A Toeplitz matrix, T (g), is an infinite dimensional matrix, which is constant along the diagonals…”

Section: The Global Error For 2-d Transportmentioning

confidence: 99%

“…The theorem of Toeplitz [1] states that the 2-norm of the infinite matrix T (g) is equal to the maximum modulus of g(e iθ ) in the interval 0 ≤ θ < 2π , i.e.…”

Section: The Global Error For 2-d Transportmentioning

confidence: 99%

Global error bounds for the Petrov-Galerkin discretization of the neutron transport equation

Chang

Greenbaum

Machorro

2010

Numer. Linear Algebra Appl.

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Abstract. In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L 2 norm at the rate of h 2 . Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.

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Introduction to Large Truncated Toeplitz Matrices

Cited by 575 publications

References 0 publications

Szegö Type Results Relative to a Sequence of Model Spaces

Szegö Type Results Relative to a Sequence of Model Spaces

Infinite-dimensional numerical linear algebra: theory and applications

Global error bounds for the Petrov-Galerkin discretization of the neutron transport equation

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