A Polynomial Fitting Problem: The Orthogonal Distances Method

- - - - - o ' " A STANDARD METHOD FOR SURFACE FITTING BY ORTHOGONAL POLYNOMIALS

An algorithm for least squares fitting of a polynomial to a function z(x.y) of two independent variables is described. It is assumed that the function is given by a number of "measured values". which may be arbitrarily distributed over the ~Yplane. The polynomial is constructed as a linear combination of a set of polynomials which are orthonormalized over the set of given data points by the mod...

solution of security constrained unit commitment problem by a new multi-objective optimization method

چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...

Fitting Distances by Least Squares

Least squares fitting of spheres and ellipsoids using not orthogonal distances

Berman [1] examined the problem of estimating the parameters of a circle when angular differences between successively measured data points were also measured. Applications were reported. Späth [4] generalized that problem by considering an ellipse. Now we will consider measured data points (xk, yk, zk) in space and also associated measured angles (uk, vk) k = 1, . . . , n > 8, for the canonica...

Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola

The least-squares "tting minimizes the squares sum of error-of-"t in prede"ned measures. By the geometric "tting, the error distances are de"ned with the orthogonal, or shortest, distances from the given points to the geometric feature to be "tted. For the geometric "tting of circle/sphere/ellipse/hyperbola/parabola, simple and robust nonparametric algorithms are proposed. These are based on th...