Complexity theory of real functions
Complexity theory of real functions
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Computing the Dimension of Linear Subspaces
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Algebraic Complexity Theory
Computability in linear algebra
Theoretical Computer Science
Stability versus speed in a computable algebraic model
Theoretical Computer Science - Real numbers and computers
Uniformly Computable Aspects of Inner Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Computability of the Spectrum of Self-Adjoint Operators and the Computable Operational Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Computing Solutions of Symmetric Hyperbolic Systems of PDE's
Electronic Notes in Theoretical Computer Science (ENTCS)
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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.