Abstract
The following problem is treated: given a set ofm rectangular regions in the plane, fit an interval polynomial of degreen>m through the regions. This is a generalization of the discrete polynomial least squares problem. Three generalizations of the standard methods for the discrete polynomial least squares are considered and compared on numerical examples. One of the methods is recommended since it gives superior results in all cases tested.
Zusammenfassung
Das folgende Problem wird behandelt: gegeben sei eine Menge vonm rechteckigen Gebieten in der Ebene, man finde ein Intervall-Polynom vom Gradn>m durch diese Gebiete. Dies ist eine Verallgemeinerung des diskreten Problems der kleinsten Quadrate. Drei Verallgemeinerungen der gewöhnlichen Methode der kleinsten Quadrate für Polynome werden betrachtet und an numerischen Beispielen verglichen. Eine dieser Methoden wird empfohlen, da sie in allen Testbeispielen bessere Ergebnisse gibt.
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Rokne, J. Polynomial least square interval approximation. Computing 20, 165–176 (1978). https://doi.org/10.1007/BF02252345
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DOI: https://doi.org/10.1007/BF02252345