A tutorial history of least squares with applications to astronomy and geodesy
Copyright policy )A tutorial history of least squares with applications to astronomy and geodesy
This paper has the character of a self-contained introduction and can at the same time serve as reference text for those in any of the various fields that use the principle of least squares. It reviews the history, development and applications of least squares. In particular, problems of ordinary, constrained, weighted and total least squares are discussed. The presentation includes the basic theory, e.g. unitary factorizations and singular-value decompositions of matrices and the matrix approximation theorems of Schmidt, Mirsky and Weyl. For sake of illustration a few numerical examples of curve and surface fitting in astronomy and geodesy are proposed.
- Western Washington University United States
- Eastern Washington University United States
History, Numerical solutions to overdetermined systems, pseudoinverses, Computational methods for problems pertaining to astronomy and astrophysics, unitary factorizations, historical survey, Least squares, Numerical mathematical programming methods, Constrained, Weighted, geodesy, Ordinary, History of mathematics in the 20th century, singular-value decompositions, numerical examples, Computational methods for problems pertaining to geophysics, curve and surface fitting, Applied Mathematics, History of numerical analysis, astronomy, Computational Mathematics, History of mathematics in the 19th century, Numerical smoothing, curve fitting, weighted and total least squares, Total
History, Numerical solutions to overdetermined systems, pseudoinverses, Computational methods for problems pertaining to astronomy and astrophysics, unitary factorizations, historical survey, Least squares, Numerical mathematical programming methods, Constrained, Weighted, geodesy, Ordinary, History of mathematics in the 20th century, singular-value decompositions, numerical examples, Computational methods for problems pertaining to geophysics, curve and surface fitting, Applied Mathematics, History of numerical analysis, astronomy, Computational Mathematics, History of mathematics in the 19th century, Numerical smoothing, curve fitting, weighted and total least squares, Total
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