Symbolic-numeric integration of rational functions
نویسندگان
چکیده
منابع مشابه
Symbolic-Numeric Integration of Rational Functions
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of ill-conditioning to which numerical methods are susceptible. We propose two alternative methods for exact input that compute the rational part of the integral using He...
متن کاملRevisiting numeric/symbolic indefinite integration of rational functions, and extensions
We know we can solve this problem: Given any rational function f(x) = p(x)/q(x), where p and q are univariate polynomials over the rationals, compute its indefinite integral, using if necessary, algebraic numbers. But in many circumstances an approximate result is more likely to be of use. Furthermore, it is plausible that it would be more useful to solve the problem to allow definite integrati...
متن کاملNumeric versus Symbolic Computation
Twentyfive years ago when I studied Physics, only one of the students who participated in a laboratory course that I took was possessing one of the first calculators to process the data we were obtaining. Believe it or not, everybody else, including me, had to use a slide-rule for this purpose. Nowadays, the calculator is used by everybody, by far not only for academic purposes. Hence it is the...
متن کاملIntegration of Rational Functions: Rational Computation of the Logarithmic Part
This formula is not satisfactory under a computing point of view because it introduces more algebraic quantities than necessary. The number P(a)/Q'(a) is called the residue of the root a of Q. We introduce the notion of multiplicity of a residue b that is the number of roots a having b as a residue. Trager (1976) introduced a new formula involving less algebraic numbers: let S(y) be the resulta...
متن کاملA symbolic-numeric silhouette algorithm
We have revisited the silhouette algorithm developed by Canny, and designed its new symbolic-numeric version. The symbolic-numeric silhouette algorithm do not require the symbolic computation of the determinants of resultant matrices, and can work on oating point arithmetic. Though its combinatorial complexity remains the same, but its algebraic complexity has been improved signi cantly which i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 2019
ISSN: 1017-1398,1572-9265
DOI: 10.1007/s11075-019-00726-6