ISSN:
1572-9125
Keywords:
Overdetermined linear systems
;
rank reduction
;
Hankel structure
;
Toeplitz structure
;
structured total least norm
;
total least squares
;
1-norm
;
2-norm
;
singular value decomposition
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the closest low rank approximation to a given matrix in matrix L 2 norm and Frobenius norm, may not be appropriate for these applications since it does not preserve the given structure. We present a new method for structure preserving low rank approximation of a matrix, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to an overdetermined linear system AX ≈ B, preserving the given linear structure in the perturbation [E F] such that (A + E)X = B + F. The approximate solution can be obtained to minimize the perturbation [E F] in the L p norm, where p = 1, 2, or ∞. An algorithm is described for Hankel structure preserving low rank approximation using STLN with L p norm. Computational results are presented, which show performances of the STLN based method for L 1 and L 2 norms for reduced rank approximation for Hankel matrices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022347425533
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