Full metadata record
DC Field | Value | Language |
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dc.contributor.author | Liu, Ching-Sung | en_US |
dc.contributor.author | Guo, Chun-Hua | en_US |
dc.contributor.author | Lin, Wen-Wei | en_US |
dc.date.accessioned | 2018-08-21T05:54:21Z | - |
dc.date.available | 2018-08-21T05:54:21Z | - |
dc.date.issued | 2017-09-01 | en_US |
dc.identifier.issn | 0029-599X | en_US |
dc.identifier.uri | http://dx.doi.org/10.1007/s00211-017-0869-7 | en_US |
dc.identifier.uri | http://hdl.handle.net/11536/145841 | - |
dc.description.abstract | We present a Newton-Noda iteration (NNI) for computing the Perron pair of a weakly irreducible nonnegative mth-order tensor A, by combining the idea of Newton's method with the idea of the Noda iteration. The method requires the selection of a positive parameter theta(k) in the kth iteration, and produces a scalar sequence approximating the spectral radius of A and a positive vector sequence approximating the Perron vector. We propose a halving procedure to determine the parameters theta(k), starting with theta(k) for each k, such that the scalar sequence is monotonically decreasing. Convergence of this sequence to the spectral radius of A (and convergence of the vector sequence to the Perron vector) is guaranteed for any initial positive unit vector, as long as the sequence {theta(k)} so chosen is bounded below by a positive constant. In this case, we always have theta(k) = 1 near convergence and the convergence is quadratic. Very often, the halving procedure will return theta(k)(= 1 i.e., no halving is actually used) for each k. If the tensor is semisymmetric, m >= 4, and theta(k) = 1, then the computational work in the kth iteration of NNI is roughly the same as that for one iteration of the Ng-Qi-Zhou algorithm, which is linearly convergent for the smaller class of weakly primitive tensors. | en_US |
dc.language.iso | en_US | en_US |
dc.title | Newton-Noda iteration for finding the Perron pair of a weakly irreducible nonnegative tensor | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1007/s00211-017-0869-7 | en_US |
dc.identifier.journal | NUMERISCHE MATHEMATIK | en_US |
dc.citation.volume | 137 | en_US |
dc.citation.spage | 63 | en_US |
dc.citation.epage | 90 | en_US |
dc.contributor.department | 應用數學系 | zh_TW |
dc.contributor.department | Department of Applied Mathematics | en_US |
dc.identifier.wosnumber | WOS:000406419200003 | en_US |
Appears in Collections: | Articles |