Computing circles and spheres of arithmitic least squares

✍ Scribed by Yves Nievergelt

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 640 KB
• Volume: 81
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(94)90082-5

✦ Synopsis

A proof of the existence and uniqueness of L. Moura and R. Kitney's circle of least squares leads to estimates of the accuracy with which a computer can determine that circle. The result shows that the accuracy deteriorates as the correlation between the coordinates of the data points increases in magnitude. Yet a numerically more stable computation of eigenvectors yields the limiting straight line, which a further analysis reveals to be the line of total least squares. The same analysis also provides generalizations to fitting spheres in higher dimensions.