On Factorization of Analytic Functions and Its Verification
On Factorization of Analytic Functions and Its Verification
复制标题
论解析函数的因式分解及其验证
DOI：
10.1023/a:1009931231719
复制
发表时间：
2000
影响因子：
--
通讯作者：
H. Sugiura
中科院分区：
文献类型：
--
作者：
T. Sakurai;H. Sugiura
提出了一种求解析函数f(Z)的多项式因子的区间方法。通过递归地使用类Samelson方法，我们得到了一个多项式序列，如果初始近似因子p(Z)充分接近top*(Z)，则多项式序列收敛到因子p*(Z)off(Z)。该方法包含了一些著名的迭代公式，并与有理逼近有密切关系。根据这种分解方法，导出了p*(Z)的一个不动点关系。基于这个关系，我们得到了一个复系数区间多项式，它包含p*(Z)。
An interval method for finding a polynomial factor of an analytic functionf(z) is proposed. By using a Samelson-like method recursively, we obtain a sequence of polynomials that converges to a factorp*(z) off(z) if an initial approximate factorp(z) is sufficiently close top*(z). This method includes some well known iterative formulae, and has a close relation to a rational approximation. According to this factoring method, a fixed point relation forp*(z) is derived. Based on this relation, we obtain a polynomial with complex interval coefficients that includesp*(z).