Abstract
In this work, we consider block-Jacobi methods with Newton steps in each subspace search and prove their local quadratic convergence to a local minimum with non-degenerate Hessian under some orthogonality assumptions on the search directions. Moreover, such a method is exemplified for non-unitary joint matrix diagonalization, where we present a block-Jacobi-type method on the oblique manifold with guaranteed local quadratic convergence.
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Notes
- 1.
That is, \(\mu _x^{-1}\) is a coordinate chart around x.
- 2.
The reason why we choose a local and not a global minimum here is that for the convergence analysis, this choice is needed to be smooth around a minimizer of the cost function. This can only be guaranteed by choosing the nearest local minimum along basic transformations.
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Kleinsteuber, M., Shen, H. (2015). Block-Jacobi Methods with Newton-Steps and Non-unitary Joint Matrix Diagonalization. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_51
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DOI: https://doi.org/10.1007/978-3-319-25040-3_51
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