O(n) Algorithms for Banded Plus Semiseparable Matrices
We present a new representation for the inverse of a matrix that is a sum of a banded matrix and a semiseparable matrix. In particular, we show that under certain conditions, the inverse of a banded plus semiseparable matrix can also be expressed as a banded plus semiseparable matrix. Using this result, we devise a fast algorithm for the solution of linear systems of equations involving such matrices. Numerical results show that the new algorithm competes favorably with existing techniques in terms of computational time.
Mathematics Subject Classification (2000)15A09 15A23 65F05 65L10 65R20
KeywordsSemiseperable matrix fast algorithms linear solver inverse structured matrices
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- T. Kailath and A.H. Sayed. Fast reliable algorithms for matrices with structure. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1999.Google Scholar
- E. Van Camp, N. Mastronardi and M. Van Barel. Two fast algorithms for solving diagonal-plus-semiseparable linear systems. Journal of Computational and Applied, 164–165:731–747, 2004.Google Scholar
- Y. Eidelman and I. Gohberg. A modification of Dewilde-van der Veen method for inversion of finite structured matrices. Linear Algebra Appl., 343–344:419–450, 2002.Google Scholar
- F.R. Gantmacher and M.G. Krein. Oscillation matrices and kernels and small vibrations of mechanical systems. AMS Chelsea publishing, 2002.Google Scholar
- Starr, Jr., Harold Page. On the Numerical Solution of One-Dimensional Integral and Differential Equations. Department of Computer Science, Yale University, New Haven, CT, 1992.Google Scholar