Abstract
Let A be a matrix of n rows and m columns, m ≦ n. and only if the columns are linearly independent, then for any vector b there exists a unique vector x minimizing the Euclidean norm of \( b - Ax,\left\| {b - Ax} \right\| = \mathop {\min }\limits_\xi \left\| {b - A\xi } \right\|\).
Prepublished in Numer. Math. 7, 338–352 (1965).
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References
Bauer, F. L.: Optimally scaled matrices. Numer. Math. 5, 73–87 (1963).
Householder, A. S.: Principles of numerical analysis. New York 1953.
Golub, G. H.: Numerical methods for solving linear least squares problems. Numer. Math. 7, 206–216 (1965).
Businger, P., and G. H. Golub: Linear least squares solutions by Householder transformations. Numer. Math. 7, 269–276 (1965). Cf. I/9.
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© 1971 Springer-Verlag Berlin Heidelberg
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Bauer, F.L. (1971). Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems. In: Bauer, F.L. (eds) Linear Algebra. Handbook for Automatic Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39778-7_9
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DOI: https://doi.org/10.1007/978-3-662-39778-7_9
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