Minimum error bounds for multidimensional spline approximation

✍ Scribed by J.B. Rosen

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 978 KB
• Volume: 5
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(71)80026-0

✦ Synopsis

Approximation of a smooth function f on a rectangular domain s C E z by a tensor product of splines of degree m is considered. A basis for the product spline is formed using a single one-dimensional spline function. The approximation is computed, using linear programming, so as to minimize the maximum error on a discrete grid $2 v C g2, with grid size h. Realistic a posteriori bounds on the error in the uniform norm are given. Convergence of the approximation to a best approximation as h ~ 0 is shown. The extension to linear boundary value problems is also discussed.