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»ã±¨ÌáÒª£ºConventional numerical method for Quadratic Eigenvalue Problems (QEPs) is: linearize as Generalized Eigenvalue Problems (GEPs) , solve the GEPs with some linear solver, and then recover the eigenpairs from those of the GEPs. This approach may encounter the following problems:

1. Stability problem. Even the eigenpair for the GEP is backward stable, the recovered eigenpair of the QEP may not be backward stable.

2. Memory problem. The size of the GEP is twice as large as the QEP.

3. Efficiency problem. Some structures and properties in QEP do not appear in the linearized GEP.

This talk will survey some recent advances in these directions.

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