# Sven-Erik Ekström I have a PhD 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).

After my PhD I was first a postdoc at Athens University of Economics and Business, Athens, Greece (Paris Vassalos), and I am currently a postdoc at Bergische Universität Wuppertal, Wuppertal, Germany (Matthias Bolten).

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

### Current plans:

My main research interest is spectral analysis of 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 for high precision linear algebra and ApproxFun.jl for function approximations), OEIS, Wolfram Alpha, Google Scholar, a MacBook Pro 13", and an iPad Pro 12.9" with Notability.

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

Contact by email for questions or collaboration.