What is the best way to approximate a function with a rational function?
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The best way to approximate a function with a rational function is by using interpolation at properly chosen points . This method, known as the Walsh method, provides the best approximation of a given analytical function . It has been shown that the result of Walsh can be generalized and applied to the order reduction of higher-order systems . Another approach is to use a sequence of rational functions of best approximation, which exists in certain cases . The position of the poles of the approximating rational functions is of central importance in both the possibility of close approximation and the degree of approximation . Additionally, a new algorithm has been introduced for approximation by rational functions, which requires no user input parameters and can be implemented in MATLAB .
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| Papers (4) | Insight |
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3 Citations | The paper discusses the use of transfer functions of multidimensional digital filters with separable denominators for approximating multivariate functions. It shows that the best approximation of a given function is one that interpolates the function at properly chosen points. |
Open access•Journal Article 2 Citations | The paper proposes an alternative extension of Megiddo's result for approximating rational functions by using an α-approximation for minimizing a nonnegative linear function subject to certain constraints. |
| The paper discusses the existence of a sequence of rational functions of best approximation in certain cases. It does not explicitly mention the best way to approximate a function with a rational function. | |
271 Citations | The paper does not provide a direct answer to the query. The paper is about introducing a new algorithm for approximation by rational functions, but it does not specify the best way to approximate a function with a rational function. |
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