On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert space

Ruslan Sharipov

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arXiv · 1902.06722

On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert space

Ruslan Sharipov

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Abstract

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The problem of approximation of these eigenvalues by eigenvalues of some linear operator in a finite-dimensional space of the dimension $s$ is considered and solved. The accuracy of the approximation obtained becomes unlimitedly high as $s\to\infty$.

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BibTeX RIS

Ruslan Sharipov. 2019-02-18. On simultaneous approximation of several eigenvalues of a semi-definite self-adjoint linear operator in a Hilbert space. https://arxiv.org/abs/1902.06722

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