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A definiteness test for Hankel matrices and their lower submatrices

Ein Test auf Definitheit für Hankel-Matrizen und ihre Untermatrizen

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Abstract

A definiteness test for a Hankel matrixR={r i+j } N i,j =0 and its lower submatrixS={r i+j+1 } N−1 i,j =0 is given. The test allows a description of all extensions ofR which preserve definiteness of bothR andS. This description in turn can be used as a definiteness test and it demonstrates a remarkable numerical stability.

Zusammenfassung

Ein Test auf gleichzeitige Definitheit einer HankelmatrixR={r i+j } N i,j =0 und ihrer UntermatrixS={r i+j+1 } N−1 i,j =0 wird angegeben. Er ermöglicht eine Beschreibung aller Erweiterungen vonR, die die Definitheit vonR undS enthalten. Diese Beschreibung wiederum kann als Definitheitstest benutzt werden. Dieser Test zeigt eine bemerkenswerte numerische Stabilität.

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Koltracht, I., Lancaster, P. A definiteness test for Hankel matrices and their lower submatrices. Computing 39, 19–26 (1987). https://doi.org/10.1007/BF02307710

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  • DOI: https://doi.org/10.1007/BF02307710

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