A Property of Euclid’s Algorithm and an Application to Padé Approximation
SIAM Journal on Applied Mathematics1978Vol. 34(4), pp. 611–615
Citations Over TimeTop 10% of 1978 papers
Abstract
If a and b are fixed polynomials with $\deg ( a ) > \deg ( b )$, we show that all solutions to the congruence $qb \equiv p( {\bmod a} )$ with $\deg ( q ) + \deg ( p ) < \deg ( a )$ can be obtained via Euclid’s algorithm. Using this result, we show that the Padé approximants to a given power series can also be obtained from Euclid’s algorithm.
Related Papers
- → GeneralizedF andG series and convergence of the power series solution of theN-body problem(1983)4 cited
- → Power-series unification and reversion(1987)3 cited
- → A new solution for natural convection about a vertical cone embedded in porous media prescribed wall temperature using, power series - Pade(2011)2 cited
- The Application of the Sum Formula of Infinite Geometric Series ∑from n=0 to ∞(ax~n)=a/(1-x) in Power Series(2005)