P-Least Squares Method of Curve Fitting

摘要

P-Least Squares (P-LS) method is Least Squares (LS) method promotion, based on the criteria of error p -squares minimal to select parameter a=(a_1, a_2, a_3…, a_n)~r, namely satisfies following constitute the curve-fitting method. Q(a)=∑[y_i-f(x_i, a)]~(2p)=min, (p=1, 2,...) and Q(a)=∑[(y_i-f(x_i, a))/y_i]~(2p)=min, (y_i≠0, p=1, 2,...) (i from 1 to m) Due to the arbitrariness of the number p, (1≤p<∞), P-LS method has a wide field of application, when p→∞, P-LS approximation translated Chebyshev optimal approximation. This paper discusses the general principles of P-LS method; provides a way to realize the general solution of PLS approximation. P-Least Squares method not only has significantly reduces the maximum error, also has solved the problems of Chebyshev approximation non-solution in some complex non-linear approximations, and also has the computation conveniently, can carry on the large-scale multi-data processing ability. This method is introduced by some examples unified in the materials science, the chemical engineering and the life body change.