A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices

D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics (2018).

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We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter q always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.
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Communications in Computational Physics
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Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. Communications in Computational Physics. 2018.
Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T. (2018). A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. Communications in Computational Physics.
@article{Richters_Lass_Walther_Plessl_Kühne_2018, title={A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}, journal={Communications in Computational Physics}, publisher={Global Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}, year={2018}}
Richters, Dorothee, Michael Lass, Andrea Walther, Christian Plessl, and Thomas Kühne. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” Communications in Computational Physics, 2018.
D. Richters, M. Lass, A. Walther, C. Plessl, and T. Kühne, “A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices,” Communications in Computational Physics, 2018.
Richters, Dorothee et al. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” Communications in Computational Physics (2018): n. pag. Print.
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