A method of construction of optimal experimental designs for the circle

An optimal design concentrated at a minimum number of points is considered for a polynomial regression experiment on the sphere. For the case of a polynomial experiment on the circle it is possible to explicitly find the parameters of an optimal minimal design if any optimal design is known.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 53, pp. 107–117, 1975.