On constructing a normal pseudo-solution to a system of linear equations with rectangular matrix (Q2773649)
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scientific article; zbMATH DE number 1710272
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On constructing a normal pseudo-solution to a system of linear equations with rectangular matrix |
scientific article; zbMATH DE number 1710272 |
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24 February 2002
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variational spline theory
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least squares problem
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modified \(QR\) factorization algorithm
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analytic spline
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rectangular matrix
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normal pseudo-solution
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degenerate matrix
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On constructing a normal pseudo-solution to a system of linear equations with rectangular matrix (English)
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A modified \(QR\) factorization algorithm is proposed. It allows us to construct a normal pseudo-solution to a system of linear algebraic equations (SLAE) for a rectangular or square degenerate matrix with the same efficiency as for SLAE with a square nonsingular matrix. As an application, the construction of an analytic spline on a degenerate mesh is studied and a modified algorithm is proposed to provide the ``best'' spline solution.
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