Solution of standard linear equations as well as matrix equations.
I am especially interested in Lyapunov matrix equations and narrow banded linear systems.
Order reduction of dynamical systems. I am particularly interested in "bad" systems for which reduced order models exists, but standard techniques will fail without warning.
Carl Christian Kjelgaard Mikkelsen: Retracing the residual curve of a Lyapunov equation solver
BIT Numerical Mathematics (accepted February 22nd, 2011) PDFPublishers copy
Carl Christian Kjelgaard Mikkelsen and Murat Manguoglu: Analysis of the truncated SPIKE algorithm
SIAM Journal of Matrix Analysis and Applications, vol. 30, no. 4, pp 1500-1519 (2008) PDFPublishers copy
Carl Christian Kjelgaard Mikkelsen: The explict Spike algorithm: Iterative solution of the reduced system
In: High Performance Scientific Computing: Algorithms and Applications
Berry, M.W., Gallivan, K. A., Gallopoulos E., Grama, A., Philippe, B. (eds)
Springer Verlag (2012) PDF
Carl Christian Kjelgaard Mikkelsen and Bo Kågström: Incomplete cyclic reduction of banded and strictly diagonally dominant linear systems
9th International Conference on Parallel Processing and Applied Mathmatics, PPAM-2011 Torun, Poland, September 11-14th 2011 PDF
Carl Christian Kjelgaard Mikkelsen and Bo Kågström: Parallel solution of narrow banded diagonally dominant linear systems
Conference on the State of the Art in Scientific and Parallel Computing, PARA-2010 Reykjavík, Iceland, June 6-9th 2010 PDF
Carl Christian Kjelgaard Mikkelsen: The uniqueness question
Mini-workshop on Local Time-Space Calculus with Applications, Oberwolfach, Germany, May 16-22th 2004
Oberwolfach Report, no. 26, pp. 1359-1360 (2004) PDF
Carl Christian Kjelgaard Mikkelsen: Numerical methods for large Lyapunov equations
Ph.D. dissertation, Department of Mathematics, Purdue University, USA (2009)
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Carl Christian Kjelgaard Mikkelsen: The Finite Difference Method as an Analytical Tool
M.Sc. thesis, Department of Mathematics, Aarhus University, Denmark (2003)
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Carl Christian Kjelgaard Mikkelsen: Any positive residual history is possible for the EKSM for Lyapunov matrix equations
Umeå University, Department of Computing Science and HPC2N, Technical Report UMINF-10.04 (2010) PDF
Carl Christian Kjelgaard Mikkelsen: Any positive residual history is possible for the Arnoldi method for Lyapunov matrix equations
Umeå University, Department of Computing Science and HPC2N, Technical Report UMINF-10.03 (2010) PDF
Carl Christian Kjelgaard Mikkelsen: The decay rate of the solution to a tridiagonal linear system with a very special right hand side
Purdue University, Department of Computer Sciences, Technical Report CSD TR #08-21 (2008) PDF
M. Naumov, M. Manguoglu, C. C. K. Mikkelsen and A. Sameh Reliability of Krylov subspace methods - A practical perspective II
Purdue University, Department of Computer Sciences, CSD TR #07-22 (2007)
M. Naumov, M. Manguoglu, C. C. K. Mikkelsen and A. Sameh Reliability of Krylov subspace methods - A practical perspective I
Purdue University, Department of Computer Sciences, CSD TR #07-21 (2007)
