---
_id: '18152'
abstract:
- lang: eng
  text: Computing the spectral decomposition of a normal matrix is among the most
    frequent tasks to numerical mathematics. A vast range of methods are employed
    to do so, but all of them suffer from instabilities when applied to degenerate
    matrices, i.e., those having multiple eigenvalues. We investigate the spectral
    representation's effectivity properties on the sound formal basis of computable
    analysis. It turns out that in general the eigenvectors cannot be computed from
    a given matrix. If however the size of the matrix' spectrum (=number of different
    eigenvalues) is known in advance, it can be diagonalized effectively. Thus, in
    principle the spectral decomposition can be computed under remarkably weak non-degeneracy
    conditions.
author:
- first_name: Martin
  full_name: Ziegler, Martin
  last_name: Ziegler
- first_name: Vasco
  full_name: Brattka, Vasco
  last_name: Brattka
citation:
  ama: 'Ziegler M, Brattka V. A Computable Spectral Theorem. In: <i>Proceedings of
    the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>. Vol
    2064. Berlin, Heidelberg; 2001:378-388. doi:<a href="https://doi.org/10.1007/3-540-45335-0_23">10.1007/3-540-45335-0_23</a>'
  apa: Ziegler, M., &#38; Brattka, V. (2001). A Computable Spectral Theorem. In <i>Proceedings
    of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>
    (Vol. 2064, pp. 378–388). Berlin, Heidelberg. <a href="https://doi.org/10.1007/3-540-45335-0_23">https://doi.org/10.1007/3-540-45335-0_23</a>
  bibtex: '@inproceedings{Ziegler_Brattka_2001, place={Berlin, Heidelberg}, title={A
    Computable Spectral Theorem}, volume={2064}, DOI={<a href="https://doi.org/10.1007/3-540-45335-0_23">10.1007/3-540-45335-0_23</a>},
    booktitle={Proceedings of the 4th Workshop on Computability and Complexity in
    Analysis (CCA’2000)}, author={Ziegler, Martin and Brattka, Vasco}, year={2001},
    pages={378–388} }'
  chicago: Ziegler, Martin, and Vasco Brattka. “A Computable Spectral Theorem.” In
    <i>Proceedings of the 4th Workshop on Computability and Complexity in Analysis
    (CCA’2000)</i>, 2064:378–88. Berlin, Heidelberg, 2001. <a href="https://doi.org/10.1007/3-540-45335-0_23">https://doi.org/10.1007/3-540-45335-0_23</a>.
  ieee: M. Ziegler and V. Brattka, “A Computable Spectral Theorem,” in <i>Proceedings
    of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>,
    2001, vol. 2064, pp. 378–388.
  mla: Ziegler, Martin, and Vasco Brattka. “A Computable Spectral Theorem.” <i>Proceedings
    of the 4th Workshop on Computability and Complexity in Analysis (CCA’2000)</i>,
    vol. 2064, 2001, pp. 378–88, doi:<a href="https://doi.org/10.1007/3-540-45335-0_23">10.1007/3-540-45335-0_23</a>.
  short: 'M. Ziegler, V. Brattka, in: Proceedings of the 4th Workshop on Computability
    and Complexity in Analysis (CCA’2000), Berlin, Heidelberg, 2001, pp. 378–388.'
date_created: 2020-08-24T10:14:06Z
date_updated: 2022-01-06T06:53:26Z
department:
- _id: '63'
doi: 10.1007/3-540-45335-0_23
intvolume: '      2064'
language:
- iso: eng
page: 378-388
place: Berlin, Heidelberg
publication: Proceedings of the 4th Workshop on Computability and Complexity in Analysis
  (CCA'2000)
publication_identifier:
  isbn:
  - '9783540421979'
  - '9783540453352'
  issn:
  - 0302-9743
publication_status: published
status: public
title: A Computable Spectral Theorem
type: conference
user_id: '15415'
volume: 2064
year: '2001'
...