带补偿Horner算法的忠实多项式求值
Faithful Polynomial Evaluation with Compensated Horner Algorithm
AI总结：
本文提出两个充分条件，确保IEEE-754浮点算术中多项式求值的忠实性，基于补偿Horner算法误差分析，并通过数值实验验证其有效性和低额外开销。
摘要：
本文提出了两个充分条件，以确保在IEEE-754浮点算术中对多项式进行忠实求值。忠实性意味着计算值是精确结果的两个浮点邻点之一；使用比经典Horner方案更精确的算法可以满足这一要求。这里提供的一个条件是基于补偿Horner算法误差分析得出的多项式条件数的先验界。第二个条件既是动态的又是经过验证的，用于在运行时检查给定求值的忠实性。数值实验说明了这两个条件的行为，并且相关的运行时间额外开销确实非常有趣。
英文摘要：
This paper presents two sufficient conditions to ensure a faithful evaluation of polynomial in IEEE-754 floating point arithmetic. Faithfulness means that the computed value is one of the two floating point neighbours of the exact result; it can be satisfied using a more accurate algorithm than the classic Horner scheme. One condition here provided is an apriori bound of the polynomial condition number derived from the error analysis of the compensated Horner algorithm. The second condition is both dynamic and validated to check at the running time the faithfulness of a given evaluation. Numerical experiments illustrate the behavior of these two conditions and that associated running time over-cost is really interesting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
