Abstract
We discuss the problem of minimizing the spectral norm of the inverse of a matrix, when a submatrix of the matrix can be chosen arbitrarily. In a recent paper by the authors [3], it was shown that the solution of this problem can be discussed in a similar way as the problem of minimizing the norm of the matrix in terms of matrix Riccati inequalities.
Here we review the results for the norm of the inverse and then apply these results to the robust regularization of descriptor control problems. We also describe a numerical method and give numerical examples.
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References
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L. Elsner, C. He, and V. Mehrmann, Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion, Tech. Rep. 92–028, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik, Universität Bielefeld, Fakultät für Mathematik.
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© 1994 Springer-Verlag New York, Inc.
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Elsner, L., He, C., Mehrmann, V. (1994). Completion of a Matrix so that the Inverse has Minimum Norm. Application to the Regularization of Descriptor Control Problems. In: Van Dooren, P., Wyman, B. (eds) Linear Algebra for Control Theory. The IMA Volumes in Mathematics and its Applications, vol 62. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8419-9_7
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DOI: https://doi.org/10.1007/978-1-4613-8419-9_7
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