The distance to the origin of a certain point set in 𝐸ⁿ
William Karush, N. Z. Wolfsohn · Proceedings of the American Mathematical Society · 1955
The restriction 0^q<m has been imposed on the side conditions (1) and this assumption will be maintained in making the proof. However it is a simple matter to verify that for w = 0, 1, 2, • • ■ , q the only point satisfying the equations (1) is (1, 0, • • • , 0). Hence we see directly that/min = l. But this value is also given by formula (2). Thus, the theorem remains valid without the restriction 0^q<m. The minimization problem described above arose in connection with a problem of linear smoothing of statistical data. Let £1, £2, £3, • • • represent an incoming sequence of values of independent random