Fast Computation of the n-th Root in Quad-double Arithmetic Using a Fourth-order Iterative Scheme

• Tsubasa, Saito

抄録

We propose new algorithms for computing the n-th root of a quad-double number. We construct an iterative scheme that has quartic convergence and propose algorithms that require only about 50% to 60% of the double-precision arithmetic operations of the existing algorithms. The proposed algorithms perform about 1.7 times faster than the existing algorithms, yet maintain the same accuracy. They are sufficiently effective and efficient to replace the existing algorithms.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.21(2013) No.2 (online)DOI http://dx.doi.org/10.2197/ipsjjip.21.315------------------------------

We propose new algorithms for computing the n-th root of a quad-double number. We construct an iterative scheme that has quartic convergence and propose algorithms that require only about 50% to 60% of the double-precision arithmetic operations of the existing algorithms. The proposed algorithms perform about 1.7 times faster than the existing algorithms, yet maintain the same accuracy. They are sufficiently effective and efficient to replace the existing algorithms.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.21(2013) No.2 (online)DOI http://dx.doi.org/10.2197/ipsjjip.21.315------------------------------

収録刊行物

• 情報処理学会論文誌

  情報処理学会論文誌 54 (3), 2013-03-15

キーワード

• [一般論文] octuple-precision, quad-double arithmetic, square root, n-th root, modified Newton's method

詳細情報

• CRID: 1050564287856574464
• NII論文ID: 110009552604
• NII書誌ID: AN00116647
• ISSN: 18827764
• Web Site: http://id.nii.ac.jp/1001/00091308/
• 本文言語コード: en
• 資料種別: journal article
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