# Sven-Erik Ekström

I have a Ph.D. in scientific computing (numerical analysis) from Uppsala University, Uppsala, Sweden, with the thesis "Matrix-Less Methods for Computing Eigenvalues of Large Structured Matrices" (full text) (Maya Neytcheva, Stefano Serra-Capizzano, and Carlo Garoni).

I have received the International postdoc grant (Spring Call 2019, 3.15 MSEK ≈ 335 kUSD) of the Swedish Research Council, and will spend the coming three years (from February 2020) at Uppsala University, Uppsala, Sweden (Maya Neytcheva), University of Insubria, Como, Italy (Stefano Serra-Capizzano), and Kent State University, Kent, USA (Lothar Reichel).

After my Ph.D. I have also been a postdoc at Athens University of Economics and Business, Athens, Greece (Paris Vassalos), and Bergische Universität Wuppertal, Wuppertal, Germany (Matthias Bolten).

### Current plans:

My main research interest is spectral analysis of matrix sequences from PDE and FDE discretizations, and other structured matrices (especially Toeplitz-like), using matrix-less methods, the theory of GLT sequences, and other techniques. I especially like non-Hermitian matrix sequences with peculiar spectral behaviour. Some current projects are,

• Parallel-in-Time (PiT): Spectral analysis of associated matrices;
• Fractional derivatives (FDE): Preconditioning for iterative solvers, and spectral analysis of discretization matrices;
• Asymptotic expansion (Matrix-less methods): Eigenvalues, eigenvectors, matrix-valued and multi-variate symbols, diagonal sampling matrices, perfect grids;
• Non-Hermitian symbols and matrix sequences: Spectral analysis of some special banded and non-banded Toeplitz and Toeplitz-like matrix sequences; e.g., $$\{T_n(f)\}_n$$ for symbols $$f(z)=-z+1+z^{-1}+z^{-2}+z^{-3}$$, $$z\in\mathbb{C}$$, $$f(z)=\alpha z^{-r}+\beta+\gamma z^s$$, $$r\neq s\in\mathbb{N}$$, $$\alpha,\beta,\gamma\in\mathbb{C}$$, or $$f(z)=z^{-1}(1-z)^\alpha$$, $$\alpha\in(1,2)$$.

My preferred research tools are Julia (with GenericLinearAlgebra.jl and GenericSchur.jl for high precision linear algebra and ApproxFun.jl for function approximations), OEIS, Wolfram Alpha, Google Scholar, a MacBook Pro 13", clusters at UPPMAX, and an iPad Pro 12.9" with Notability.

In my spare time I enjoy packrafting, collecting tools, art, books, and artifacts, and restoring my house Lilla Säteriet (built 1819) located in Ekeby by.

Contact by email for questions or collaboration.