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Inertia-preserving secant updates. (English) Zbl 0651.65041

A class of rank-two inertia-preserving updates for symmetric matrices \(H_ c\) is studied. To ensure that inertia is preserved, the updates are chosen to be of the form \(H_+=FH_ cF^ t\), where \(F=I+qr^ t\), with q and r selected so that the secant equation is satisfied. A characterization is given for all such updates. Using a parametrization of this family of updates, the connection between them and the Broyden class of updates is established. Also, parameter selection criteria that can be used to choose the optimally conditioned update or the update closest to the SR1 update are discussed.
Reviewer: C.A.Beattie

MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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