Geodesic
On the construction of a normal pseudo-solution for a~system of linear equations with a~rectangular matrix
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 285-293.

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A modified $QR$ factorization algorithm is proposed. It allows us to construct a normal pseudo-solution of 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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A. I. Rozhenko. On the construction of a normal pseudo-solution for a~system of linear equations with a~rectangular matrix. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 285-293. http://geodesic.mathdoc.fr/item/SJVM_2001_4_3_a6/

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