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Computation of the L∞-Norm via Interpolation

This algorithm is based on Hermite interpolation of the given L-function on the imaginary axis to obtain a sequence of reduced approximations of the function whose L-norms converge to the L-norm of the original function. The norm values of the reduced functions are computed by established methods for the small-scale case. In case of convergence, a superlinear rate of convergence has been shown. Moreover, in version 1.1, rational interpolation using Loewner matrices has been implemented. In case of irrational functions, this can lead to large performance gains.


Intermediate reduced functions and their L-norms


  • Nicat Aliyev, Emre Mengi (Koç University, Istanbul, Turkey)
  • Paul Schwerdtner, Matthias Voigt (TU Berlin)


Version 1.0

Version 1.1

Version 1.2

License and Usage

This software is published under the GNU General Public License, version 3. It is research code and there is no warranty for correctness of numerical results. This software uses the MATLAB package eigopt by Emre Mengi, Emre Alper Yıldırım, and Mustafa Kılıç and SLICOT, version 5.6, which underlie own conditions. If you use this code for your own work, then please cite the publications stated below.


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