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Surface Approximation and Interpolation via Matrix SVD

A lesser known application of the SVD. First Paragraph: Applications of mathematics and statistics often require finding a smooth approximation to a finite set of data points, or interpolating the data points. Mathematicians frequently use cubic spline interpolation when the points lie in a plane, whereby the points are connected with a continuous curve made up of cubic polynomials pieced together in such a way that the combined curve has coninuous first and second derivatives at the junction points. There are many other interpolation techniques, such as Lagrange polynomials and Hermite cubics. Furthermore, when the data points are at all uncertain, smoothing procedures such as a least square approximation may be preferable to exact interpolation. Our interest here is in showing how to extend such planar techniques to handle three-dimensional data points, by using the Singular Value Decomposition (SVD) of a matrix.

Identifier: 
http://www.jstor.org/stable/pdfplus/2687215.pdf
Subject: 
Rating: 
Average: 4.5 (2 votes)
Creator(s): 
Andrew E. Long and Clifford A. Long
Cataloger: 
Daniel Drucker
Publisher: 
The College Mathematics Journal 32 No. 1 (2001), 20–25.
Rights: 
Andrew E. Long and Clifford A. Long
Format Other: 
The version at the URL given is missing the references.

Comments

meade's picture

A nice introduction to surface approximation based on the SVD. Well written, easy to read. Should be accessible to students. Could be the basis for a student project, with results rendered on a 3D printer?

drucker@math.wayne.edu's picture

Non-standard application of the SVD.

Dummy View - NOT TO BE DELETED