Efficient C++ Implementations of Generalized Interpolation in Reproducing Kernel Hilbert Spaces to Compute Lyapunov Functions | IEEE Conference Publication | IEEE Xplore

Efficient C++ Implementations of Generalized Interpolation in Reproducing Kernel Hilbert Spaces to Compute Lyapunov Functions


Abstract:

The Radial Basis Function (RBF) method to compute Lyapunov functions for nonlinear systems uses generalized interpolation in Reproducing Kernel Hilbert spaces. We present...Show More

Abstract:

The Radial Basis Function (RBF) method to compute Lyapunov functions for nonlinear systems uses generalized interpolation in Reproducing Kernel Hilbert spaces. We present two different implementation in C++. One that is computationally efficient and one that is memory efficient. The former uses standard functions of a numerical library and the latter directly calls LAPACK routines for packed matrices to perform in-place Cholesky factorization of the interpolation matrix. The memory efficient implementation only needs one-fourth of the memory needed when using a standard numerical library and thus makes it possible to use double the amount of collocation points. Both implementations are easily adapted to different generalized interpolation problems.
Date of Conference: 25-28 June 2024
Date Added to IEEE Xplore: 24 July 2024
ISBN Information:
Conference Location: Stockholm, Sweden

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