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A class of strongly stable approximation for unbounded operators

Annotation

We derive new sufficient conditions to solve the spectral pollution problem by using the generalized spectrum method. This problem arises in the spectral approximation when the approximate matrix may possess eigenvalues which are unrelated to any spectral properties of the original unbounded operator. We develop the theoretical background of the generalized spectrum method as well as illustrate its effectiveness with the spectral pollution. As a numerical application, we will treat the Schr¨odinger’s operator where the discretization process based upon the Kantorovich’s projection.

Keywords

eigenvalue approximation; spectral pollution; generalized spectrum approximation, Schr¨odinger operator

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DOI

10.20310/1810-0198-2019-24-126-218-234

UDC

517.984

Pages

218-234

References

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Received

2019-02-15

Section of issue

Scientific articles

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