Geodesic
On exponential approximation
Applications of Mathematics, Tome 30 (1985) no. 5, pp. 321-331
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One has to find a real function $y(x_1,x_2,\dots ,x_n)$ of variables $x_i$, $i=1,2,\dots,x_n). If the distribution of the values has an exponential character, then it is of advantage to choose the approximation function in the form $y(x;i)=\Pi^p_{j=0}a(i^j)^{\Pi(x_1,\dots,x_n)}$ which gives better results than other functions (e.g. polynomials). In this paper 3 methods are given: 1. The least squares method adapted for the exponential behaviour of the function. 2. The cumulated values method, following the so-called King's formula. 3. The polynomial method mentioned only for comparison. A numerical example is given in which the accuracy of all the three methods is compared.
One has to find a real function $y(x_1,x_2,\dots ,x_n)$ of variables $x_i$, $i=1,2,\dots,x_n). If the distribution of the values has an exponential character, then it is of advantage to choose the approximation function in the form $y(x;i)=\Pi^p_{j=0}a(i^j)^{\Pi(x_1,\dots,x_n)}$ which gives better results than other functions (e.g. polynomials). In this paper 3 methods are given: 1. The least squares method adapted for the exponential behaviour of the function. 2. The cumulated values method, following the so-called King's formula. 3. The polynomial method mentioned only for comparison. A numerical example is given in which the accuracy of all the three methods is compared.
DOI : 10.21136/AM.1985.104160
Classification : 41A30, 41A63
Keywords: exponential approximation 
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Huťa, Anton. On exponential approximation. Applications of Mathematics, Tome 30 (1985) no. 5, pp. 321-331. doi: 10.21136/AM.1985.104160

[1] A. Huťa: On exponential interpolation. Acta Facultatis Rerum Naturalium Universitatis Conienianae, Mathematica XXXV (1979), 157-183. | MR

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