Algorithm 694: a collection of test matrices in MATLAB
ACM Transactions on Mathematical Software (TOMS)
A stochastic arithmetic for reliable scientific computation
Mathematics and Computers in Simulation
An Efficient Stochastic Method for Round-Off Error Analysis
Proceedings of the Symposium on Accurate Scientific Computations
Stochastic arithmetic: addition and multiplication by scalars
Applied Numerical Mathematics
Numerical study of algebraic solutions to linear problems involving stochastic parameters
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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A simple algorithm for the computation of eigenvalues of real or complex square matrices is proposed. This algorithm is based on an additive decomposition of the matrix. A sufficient condition for convergence is proved. It is also shown that this method has many properties of the QR algorithm : it is invariant for the Hessenberg form, shifts are possible in the case of a null element on the diagonal. Some other interesting experimental properties are shown. Numerical experiments are given showing that most of the time the behavior of this method is not much different from that of the QR method, but sometimes it gives better results, particularly in the case of a bad conditioned real matrix having real eigenvalues.