# STAR LANCZOS

A Lanczos-like Method for the Time-Ordered Exponential

## ABOUT THE PROJECT

Solving systems of linear ordinary differential equations with variable coefficients remains a challenge that can be expressed using the so-called time-ordered exponential (TOE). The project aims at developing new numerical approximation methods for very large TOEs. Among their many applications, TOEs can be used for magnetic resonance techniques (NMR, DNP). They require a precise understanding of the quantum dynamics of spins which, mathematically, are described by a TOE. Since large spin systems are still an elusive problem, the success of the project can lead to unprecedented descriptions of NMR/DNP processes. Desired numerical methods will be designed following a recently introduced approach known as *-Lanczos; see bibliography below.

The project is funded by the 5th round of the PRIMUS Research Programme, Charles University and it will take place at the Department of Numerical Mathematics, Faculty of Mathematics and Physics, from January 2021 to December 2023.

## BIBLIOGRAPHY

### P-L. Giscard, S. Pozza, Lanczos-like method for the time-ordered exponential, arXiv:1909.03437 [math.NA], March 2020.

### P-L. Giscard, S. Pozza, Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method, arXiv:2002.06973 [math.CA], June 2020.

### P-L. Giscard, S. Pozza, Lanczos-like algorithm for the time-ordered exponential: The ∗-inverse problem, arXiv:1910.05143 [math.NA], December 2019.

## GET IN TOUCH

Department of Numerical Mathematics

Faculty of Mathematics and Physics

Charles University

Sokolovská 83

186 75 Praha 8

http://karlin.mff.cuni.cz/~pozza/