A tutorial history of least squares with applications to astronomy and geodesy

DOI10.1016/S0377-0427(00)00343-5zbMath0977.65029WikidataQ127754394 ScholiaQ127754394MaRDI QIDQ1587394

Yves Nievergelt

Publication date: 5 March 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical exampleshistorical surveygeodesyastronomycurve and surface fittingsingular-value decompositionsunitary factorizationsweighted and total least squares

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical mathematical programming methods (65K05) History of mathematics in the 20th century (01A60) Computational methods for problems pertaining to geophysics (86-08) History of mathematics in the 19th century (01A55) Computational methods for problems pertaining to astronomy and astrophysics (85-08) History of numerical analysis (65-03)

Related Items

A numerical optimization approach to generate smoothing spherical splines, A robust high-order mixed \(L^2\)-\(L^{\infty}\) estimation for linear-in-the-parameters models, Approximation of distributions by bounded sets, Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares

Uses Software

• mctoolbox
• KELLEY
• VanHuffel

Cites Work

• An Analysis of the Total Least Squares Problem
• A generalization of the Eckart-Young-Mirsky matrix approximation theorem
• Circle fitting by linear and nonlinear least squares
• Schmidt-Mirsky matrix approximation with linearly constrained singular values
• Computing circles and spheres of arithmetic least squares
• The condition of Steffensen's acceleration in several variables
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• An Algorithm for Least-Squares Circle Fitting to Data with Specified Uncertainty Ellipses
• Computing Geodetic Coordinates
• On the Early History of the Singular Value Decomposition
• Reading the Master: Newton and the Birth of Celestial Mechanics
• Inductive Proof of the Simplex Method
• Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
• Numerical Linear Algebra
• Least-squares fitting of circles and ellipses
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