Least squares algorithms for finding solutions of overdetermined linear equations which minimize error in an abstract norm
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In this paper overdetermined linear equations inn unknowns are considered. Ifm is the number of equations, let ℝ m be equipped with a smooth strictly convex norm, ‖·‖. Algorithms for finding “best-fit” solutions of the system which minimize the ‖·‖-error are given. The algorithms are iterative and in particular apply to the important case where ℝ m is given thel p -norms, (1<p<∞). The algorithms consist of obtaining a least square solution i.e. carrying out an orthogonal projection at each stage of the iteration and solving a non-linear equation in a single real variable. The convergence of the algorithms are proved in the paper.
KeywordsLinear Equation Mathematical Method Orthogonal Projection Real Variable Important Case
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