In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of...
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In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.
numerical approximate computations can solve large and complex problems *** have the advantage of high *** they only give approximate results,whereas we need exact results in some *** is a gap between approximate comp...
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numerical approximate computations can solve large and complex problems *** have the advantage of high *** they only give approximate results,whereas we need exact results in some *** is a gap between approximatecomputations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
We present a new algorithm for reconstructing an exact algebraic number from its approximate value by using an improved parameterized integer relation construction method. Our result is consistent with the existence o...
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ISBN:
(纸本)9781605586649
We present a new algorithm for reconstructing an exact algebraic number from its approximate value by using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial of an algebraic number by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with the subsistent methods, our method combines advantage of high efficiency in numericalcomputation, and exact, stable results in symbolic computation. The experimental results show that the method is more efficient than identify in Maple for obtaining an exact algebraic number from its approximation. Moreover, the Digits of our algorithm is far less than the LLL-lattice basis reduction technique in theory. In this paper, we completely implement how to obtain exact results by numerical approximate computations.
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