Chipman pseudoinverse of matrix, its computation and application in spline theory. (English) Zbl 1046.65028

The author describes the basic properties of the Chipman pseudoinverse of an arbitrary rectangular matrix. This generalizes the classical Moore-Penrose one, \(A^+\), by considering two energy scalar products, generated by two symmetric and positive definite matrices, instead of the Euclidean ones in the finite dimensional Euclidean spaces corresponding to the dimensions of the matrix. An iterative algorithm, which generalizes Greville’s one for \(A^+\) is presented for the construction of Chipman pseudoinverse.


65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F05 Direct numerical methods for linear systems and matrix inversion
15A09 Theory of matrix inversion and generalized inverses
41A15 Spline approximation
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