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We present a complete algorithm for finding an exact minimal polynomial fromits approximate value by using an improved parameterized integer relationconstruction method. Our result is superior to the existence of errorcontrolling on obtaining an exact rational number from its approximation. Thealgorithm is applicable for finding exact minimal polynomial of an algebraicnumber by its approximate root. This also enables us to provide an efficientmethod of converting the rational approximation representation to the minimalpolynomial representation, and devise a simple algorithm to factor multivariatepolynomials with rational coefficients.  Compared with the subsistent methods, our method combines advantage of highefficiency in numerical computation, and exact, stable results in symboliccomputation. we also discuss some applications to some transcendental numbersby approximations. Moreover, the Digits of our algorithm is far less than theLLL-lattice basis reduction technique in theory. In this paper, we completelyimplement how to obtain exact results by numerical approximate computations.

A complete algorithm to find exact minimal polynomial by approximations