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Linear least squares problems with additional constraints and an application to scattered data approximation. (English) Zbl 1281.65064
Summary: We construct generalized inverses to solve least squares problems with partially prescribed kernel and image spaces. To this end, we parameterize a special subset of all \((1, 3)\)-generalized inverses, and analyze their properties. Furthermore, we discuss an application to scattered data approximation where certain \((1, 3)\)-generalized inverses are more adequate than the Moore-Penrose inverse.
MSC:
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A09 Theory of matrix inversion and generalized inverses
65F10 Iterative numerical methods for linear systems
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