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Negative Pivots in Eigenvalue Extraction

Negative pivots can occur during the solution phase of an eigenvalue extraction as a result of the shifting mechanism used during a RANGE analysis (the range specified is divided into a number sections, with their origin called shift points). An eigenvalue extraction based on the Subspace method does not use shift points (unless specified) and will not output such pivots warnings.

The Lanczos algorithm introduced in version 12 will also give negative pivots.

In both cases the number of negative pivots reported in the output file equals the number of eigenvalues which exist below the first shift point currently being used.

Thus negative pivots in a "shifted" eigenvalue analysis are commonly expected and may be ignored. If they existed in the linear static analysis which should always be run first then investigation will be necessary. See here for more detail on negative pivots in general, together with a checklist of common causes.

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