Simultaneous Iteration Method for Symmetric Matrices

  • H. Rutishauser
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


The “ordinary” iteration method with one single iteration vector (sometimes called v. Mises-Geiringer iteration) can often yield an eigenvector and its eigenput value in very short time. But since this cannot be guaranteed, not even with improvements such as shifts of origin, Aitken-Wynn acceleration or Richardson’s purification, the method cannot be recommended for general use. In order to prevent possible poor convergence, the computation is carried in parallel with several iteration vectors, between which an orthogonality relation is maintained.


Iteration Step Acceptance Test Rayleigh Quotient Jacobi Method Roundoff Error 
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© Springer-Verlag Berlin · Heidelberg 1971

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  • H. Rutishauser

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