# Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems

@article{Bogoya2022FineSE, title={Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems}, author={Mauricio Bogoya and Sergei M. Grudsky and Stefano Serra Capizzano and Cristina Tablino Possio}, journal={ArXiv}, year={2022}, volume={abs/2112.02681} }

In the present article we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs). From one side they could look standard, since they are real, symmetric and positive definite. On the other hand they cause specific difficulties which prevent the successful use of classical tools. In particular the associated matrix-sequence, with respect to the matrix-size, is ill-conditioned and it is such that a…

## One Citation

### On the extreme eigenvalues and asymptotic conditioning of a class of Toeplitz matrix-sequences arising from fractional problems

- MathematicsLinear and Multilinear Algebra
- 2022

The analysis of the spectral features of a Toeplitz matrix-sequence { Tn(f) } n∈N, generated by a symbol f ∈ L([−π, π]), real-valued almost everywhere (a.e.), has been provided in great detail in the…

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