Abstract
For the given data ( w i , x i , y i ) , i = 1 , … , M , we consider the problem of existence of the best discrete approximation in l p norm ( 1 ≤ p < ∞ ) by reciprocals of real polynomials. For this problem, the existence of best approximations is not always guaranteed. In this paper, we give a condition on data which is necessary and sufficient for the existence of the best approximation in l p norm. This condition is theoretical in nature. We apply it to obtain several other existence theorems very useful in practice. Some illustrative examples are also included.
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