1994 | WALTER GANDER, GENE H. GOLUB and ROLF STREBEL
This paper by Walter Gander, Gene H. Golub, and Rolf Strebel presents several algorithms for fitting circles and ellipses to given points in the plane using the least-squares method. The authors compare these algorithms with classical simple and iterative methods. The focus is on finding the ellipse that minimizes the sum of the squares of the distances from the given points to the curve. The paper introduces the Gauss-Newton method to solve the nonlinear least-squares problem iteratively. It also discusses the algebraic representation of curves and the parametric form, which is suitable for minimizing the sum of squared distances. The paper dedicates its content to Åke Björck on his 60th birthday, acknowledging his significant contributions to numerical solutions of least-squares problems. The first section covers the preliminaries and introduction, defining the terms "geometric fit" and "algebraic fit," and explaining the Gauss-Newton method. The second section focuses on fitting a circle, detailing the algebraic representation and the linear system of equations used to compute the coefficients.This paper by Walter Gander, Gene H. Golub, and Rolf Strebel presents several algorithms for fitting circles and ellipses to given points in the plane using the least-squares method. The authors compare these algorithms with classical simple and iterative methods. The focus is on finding the ellipse that minimizes the sum of the squares of the distances from the given points to the curve. The paper introduces the Gauss-Newton method to solve the nonlinear least-squares problem iteratively. It also discusses the algebraic representation of curves and the parametric form, which is suitable for minimizing the sum of squared distances. The paper dedicates its content to Åke Björck on his 60th birthday, acknowledging his significant contributions to numerical solutions of least-squares problems. The first section covers the preliminaries and introduction, defining the terms "geometric fit" and "algebraic fit," and explaining the Gauss-Newton method. The second section focuses on fitting a circle, detailing the algebraic representation and the linear system of equations used to compute the coefficients.