• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.51-64
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• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.

• East Asian mathematical journal
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• v.15 no.2
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• pp.345-354
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• 1999

Orthogonalization can be done by the well known Gram-Schmidt process or by using Householder transformations. In this paper, we introduced an alternative process using linear systems.

• The Transactions of the Korea Information Processing Society
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• v.5 no.4
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• pp.959-966
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• 1998

We present fast QR factorization algorithms $m{\times}n\;(m{\geq}n)$ Toeplitz matrix. These QR factorization algortihms are determined from the shift-invariance properties of underlying matrices. The major transformation tool is a stabilized/hyperbolic Householder transformation. The algortihms require O(mn) operations, and can be easily implemented on distributed-memory multiprocessors.