Summary
A method of determining the best approximation by an alternating family on an interval is by approximating on finite subsets of the interval. In this note we show that this method can fail to converge, particularly in the case of polynomial rational approximation and exponential approximation when the best approximation is degenerate.
Zusammenfassung
Eine Methode, die beste Approximation durch eine alternierende Familie auf einem Intervall zu bestimmen, ist, auf endliche Teilmengen des Intervalls zu approximieren. In dieser Note zeigen wir, daß diese Mettode nicht zu konvergieren braucht, insbesondere nicht im Falle der rationalen Polynomapproximation und der exponentiellen Approximation, wenn die beste Approximation entartet ist.
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Dunham, C.B. Approximation by alternating families on subsets. Computing 9, 261–265 (1972). https://doi.org/10.1007/BF02241601
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DOI: https://doi.org/10.1007/BF02241601