On nonlinear functions of linear combinations
Projection pursuit algorithms approximate a function of $p$ variables by a sum of nonlinear functions of linear combinations: \[ (1)\qquad f\left( {x_1 , \cdots ,x_p } \right) \doteq \sum_{i = 1}^n {g_i \left( {a_{i1} x_1 + \cdots + a_{ip} x_p } \right)} . \] We develop some approximation theory, gi...
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| Veröffentlicht in: | SIAM journal on scientific and statistical computing 1984-03, Vol.5 (1), p.175-191 |
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| container_title | SIAM journal on scientific and statistical computing |
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| creator | DIACONIS, P MEHRDAD SHAHSHAHANI |
| description | Projection pursuit algorithms approximate a function of $p$ variables by a sum of nonlinear functions of linear combinations: \[ (1)\qquad f\left( {x_1 , \cdots ,x_p } \right) \doteq \sum_{i = 1}^n {g_i \left( {a_{i1} x_1 + \cdots + a_{ip} x_p } \right)} . \] We develop some approximation theory, give a necessary and sufficient condition for equality in (1), and discuss nonuniqueness of the representation. |
| doi_str_mv | 10.1137/0905013 |
| format | Article |
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| identifier | ISSN: 0196-5204 |
| ispartof | SIAM journal on scientific and statistical computing, 1984-03, Vol.5 (1), p.175-191 |
| issn | 0196-5204 1064-8275 2168-3417 1095-7197 |
| language | eng |
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| source | SIAM Journals Online |
| subjects | Algorithms Approximation Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Polynomials Sciences and techniques of general use |
| title | On nonlinear functions of linear combinations |
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