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- W2624073386 abstract "Let the scalars $A^{(j)}_n$ be defined via the linear equations $$A_l=A^{(j)}_n+sum^n_{k=1}bar{alpha}_ku_{k+l-1}, l=j,j+1,ldots,j+n .$$ Here the $A_i$ and $u_i$ are known and the $bar{alpha}_k$ are additional unknowns, and the quantities of interest are the $A^{(j)}_n$. This problem arises, for example, when one computes infinite-range integrals by the higher-order $G$-transformation of Gray, Atchison, and McWilliams. One efficient procedure for computing the $A^{(j)}_n$ is the rs-algorithm of Pye and Atchison. In the present work, we develop yet another procedure that combines the FS-algorithm of Ford and Sidi and the qd-algorithm of Rutishauser, and we denote it the FS/qd-algorithm. We show that the FS/qd-algorithm has a smaller operation count than the rs-algorithm. We also show that the FS/qd algorithm can also be used to implement the transformation of Shanks, and compares very favorably with the $varepsilon$-algorithm of Wynn that is normally used for this purpose." @default.
- W2624073386 created "2017-06-15" @default.
- W2624073386 creator A5067073885 @default.
- W2624073386 date "2017-06-06" @default.
- W2624073386 modified "2023-09-27" @default.
- W2624073386 title "A New Algorithm for the Higher-Order $G$-Transformation" @default.
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