• Corpus ID: 235352773

When does the Lanczos algorithm compute exactly?

@article{Simonov2021WhenDT,
  title={When does the Lanczos algorithm compute exactly?},
  author={Dorota Simonov{\'a} and Petr Tich'y},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.02068}
}
In theory, the Lanczos algorithm generates an orthogonal basis of the corresponding Krylov subspace. However, in finite precision arithmetic, the orthogonality and linear independence of the computed Lanczos vectors is usually lost quickly. In this paper we study a class of matrices and starting vectors having a special nonzero structure that guarantees exact computations of the Lanczos algorithm whenever floating point arithmetic satisfying the IEEE 754 standard is used. Analogous results are… 
1 Citations
Low-memory Krylov subspace methods for optimal rational matrix function approximation
TLDR
The Lanczos method for optimal rational matrix function approximation (Lanczos-OR) returns the optimal approximation from a Krylov subspace in a norm induced by the rational function’s denominator, and can be computed using the information from a slightly larger KrylovSubspace.

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