Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute...
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Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton＇s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.
Based on an improved parameterized integer relation construction method, a complete algorithm is proposed for finding an exact minimal polynomial from its approximate root. It relies on a study of the error controllin...
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Based on an improved parameterized integer relation construction method, a complete algorithm is proposed for finding an exact minimal polynomial from its approximate root. It relies on a study of the error controlling for its approximation. We provide a sufficient condition on the precision of the approximation, depending only on the degree and the height of its minimal polynomial. Our result is superior to the existent error controlling on obtaining an exact rational or algebraic number from its approximation. Moreover, some applications are presented and compared with the subsistent methods.
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