On computing the eigenvectors of structured matrices
AuthorKodal Sevindir, Hülya
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CitationKodal Sevindir, H. (2009). On computing the eigenvectors of structured matrices. Maltepe Üniversitesi. s. 201.
A numerical method for computing the eigenvectors of symmetric tridiagonal matrices is studied in this paper. This method can easily be adapted for other classes of matrices, e.g. semiseparable matrices, as long as a step of the QR method requires O(n) floating point operations. A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric structured one, i.e., tridiagonal matrices or semiseparable matrices. This step is accomplished in O(n 3 ) operations. Once the latter symmetric structured matrix is available, its spectrum is computed in an iterative fashion by means of the QR method in O(n 2 ) operations. In principle, the whole set of eigenvectors of the latter structured matrix can be computed by means of inverse iteration in O(n 2 ) operations.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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