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The Faculty of Informatics is pleased to announce a seminar given by Matthias Bollhöfer



Approximate Selective Matrix Inversion Algorithms for Computing the Diagonal Entries of the Inverse Matrix
Speaker: Matthias Bollhöfer
TU Braunschweig, Germany
Date: Tuesday, October 6, 2015
Place: USI Lugano Campus, room SI-003, Informatics building (Via G. Buffi 13)
Time: 15:30



Functions of entries of inverses of matrices like all diagonal entries of a sparse matrix inverse or its trace arise in several important computational applications such as density functional theory [2], covariance matrix analysis in uncertainty quantification [1] or when evaluating Green's functions in computational nanolelectronics [4].

We will present algorithms for (approximately) computing selective parts of the matrix inverse such as the diagonal part. The core part of this algorithm uses an approximate version of the SelInv method by Lin et al [3]. We will discuss modifications of this algorithm to make it applicable for incomplete factorization methods. Among these are inverse awareness of the compute incomplete triangular factor as well as eigenvector deflation techniques. Its overall performance will be demonstrated for selected numerical examples, in particular for symmetric and indefinite application problems which frequently arise from practical applications.



[1] C. Bekas, A. Curioni, and I. Fedulova. Low-cost high performance uncertainty quantification. Concurrency and Computation: Practice and Experience, 2011.

[2] W. Kohn, L. Sham, et al. Self-consistent equations including exchange and correlation effects. Phys. Rev, 140(4A):A1133-A1138, 1965.

[3] L. Lin, C. Yang, J.C. Meza, J. Lu, L. Ying, and W. E. SelInv - an algorithm for selected inversion of a sparse symmetric matrix. ACM Transactions on Mathematical Software}, 37(4):40:1-40:19, 2011.

[4] M. Luisier, T. Boykin, G. Klimeck, and W. Fichtner. Atomistic nanoelectronic device engineering with sustained performances up to 1.44 pflop/s. In High Performance Computing, Networking, Storage and Analysis (SC), 2011 International Conference for, pages 1-11. IEEE, 2011.



Current affiliation: professor for numerical mathematics at TU Braunschweig (since 2006). Habilitation: venia legendi for Mathematics at TU Berlin, 2003. PhD: PhD in Mathematics at TU Chemnitz, 1998.
Research field: Numerical analysis, preconditioning methods in particular those based on incomplete factorizations, or approximate inverses or multilevel-based, scientific computing, model order reduction methods, hierarchical matrices.
Co-authored software: ILUPACK (multilevel incomplete factorization package), JADAMILU, (symmetric eigenvalue computation package based on preconditioned Jacobi-Davidson methods).


Host: Prof. Olaf Schenk


Faculty of Informatics

Faculty of Informatics
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH-6904 Lugano
Tel.: +41 (0)58 666 46 90
Fax: +41 (0)58 666 45 36
Email: decanato.inf@usi.ch
Web: www.inf.usi.ch
Twitter: @USI_INF


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