Quasi‐periodic (QP) VLF emissions are noise bursts repeated at intervals of the order of 30 sec. This period is substantially longer than the ∼2‐sec two‐hop whistler mode travel time along the associated magnetospheric field‐aligned paths. New details of QP emissions, particularly of interactions between whistlers and QP activity, have been found in a study of VLF recordings from Eights, Antarctica (L ∼ 4), during the period November 1964 to October 1965. The occurrence statistics show that QP emissions favor the equinoxes, later afternoon hours, and quiet geomagnetic conditions. Emission frequencies generally lie between ∼1.5 and 4 kHz. Detailed studies of broad band VLF spectra show that QP emissions are strongly affected by whistlers. Whistlers often disrupt well‐behaved QP patterns by suddenly increasing the QP period, by terminating the emission altogether, or by modifying the fine structure of QP bursts (this fine structure frequently consists of periodic VLF emissions and/or VLF chorus elements). Whistlers can sometimes initiate QP emissions by modulating multiphase periodic emissions. When there are strong interactions between QP emissions and whistlers, QP emissions and whistler echo trains have the same time rate of change of upper cutoff frequency. This evidence of complex connections among various types of VLF signals in the magnetosphere adds a new dimension to recent discoveries of transient whistler‐induced precipitation of particles into the ionosphere.

Summary.The acceleration by Tchebychev iteration for solving nonsymmetric eigenvalue problems is dicussed. A simple algorithm is derived to obtain the optimal ellipse which passes through two eigenvatues in a complex plane relative to a reference complex eigenvalue. New criteria are established to identify the optimal ellipse of the eigenspectrum. The algorithm is fast, reliable and does not require a search for all possible ellipses which enclose the spectrum. The procedure is applicable to nonsymmetric linear systems as well.

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Clustering, Kernel,

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