COMPUTING CIRCLES AND SPHERES OF ARITHMETIC LEAST-SQUARES

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.