Interpolation by Ridge Functions

✍ Scribed by D. Braess; A. Pinkus

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 615 KB
• Volume: 73
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1993.1039

✦ Synopsis

We consider the problem of interpolation by linear combinations of ridge functions. A ridge function is a function of the form (f(\mathbf{a} \cdot \mathbf{x})) where (f: \mathbb{R} \rightarrow \mathbb{R}, \mathbf{a} \in \mathbb{R}^{d} \backslash{\mathbf{0}}) is a fixed vector, and (\mathbf{x} \in \mathbb{R}^{d}) is the variable. The solvability of the interpolation problem is characterized by geometric properties. 1993 Academic Press. Inc.