A parallel algorithm for the eigenvalues and eigenvectors of a general complex matrix | Zendy

Gautam Shroff | Zendy

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A parallel algorithm for the eigenvalues and eigenvectors of a general complex matrix

Author(s) -

Gautam Shroff

Publication year - 1990

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/bf01385654

Subject(s) - eigenvalues and eigenvectors , mathematics , rate of convergence , algorithm , quadratic equation , parallel algorithm , convergence (economics) , norm (philosophy) , matrix (chemical analysis) , matrix norm , computer science , geometry , key (lock) , physics , materials science , quantum mechanics , composite material , computer security , political science , law , economics , economic growth

A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this problem typically display only linear convergence, Sequential `norm-reducing' algorithms also exist and they display quadratic convergence in most cases. The new algorithm is a parallel form of the `norm-reducing' algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures. In particular, the algorithm can be implemented usingn2/4 processors, takingO(n log2n) time for random matrices.

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