While numerical (e.g. Fortran) code generation from computer algebra is nowadays relatively easy to do, the expressions as they are produced via computer algebra typically benefit from non-trivial reformulation for efficiency and numerical stability. To assist in automatic "expert reformulation", we desire good automated tools to assess the stability of a particular form of an expression. In this paper, we discuss an approach to proofs of numerical stability (with respect to roundoff error) of rational expressions. The proof technique is based upon the ability to propagate properties such as sign, exact representability, or a certain kind of numerical stability, to floating point results from properties of their antecedents.
rnThe qualitative approach to numerical stability (inspired by [12]) lends itself to implementation as a backwards-chaining theorem prover. While it is not a replacement for alternative forms of stability analysis, it can sometimes discover stability and explain it straightforwardly.
虽然如今从计算机代数生成数字(例如Fortran)代码相对容易,但是通过计算机代数生成的表达式通常受益于非平凡的重构,以提高效率和数值稳定性。为了帮助自动进行“专家重构”,我们需要一种好的自动化工具来评估特定形式的表达式的稳定性。在本文中,我们讨论了一种有理表达式的数值稳定性证明(关于舍入误差)的方法。证明技术基于将符号,精确可表示性或某种数值稳定性等属性传播到由其前项的属性产生的浮点结果的能力。 P> rn
数值稳定性的定性方法(由[12]启发)很适合作为反向链定理证明者来实现。尽管它不能替代其他形式的稳定性分析,但有时可以发现稳定性并直接对其进行解释。 P>
Univ. of Tennessee, Knoxville;
机译:使用Eckart框架的曲线内坐标中的旋转振动哈密顿量作为幂级数的数值构造的自动微分方法
机译:阐明等价的句法和数值观点:有理表达式的情况
机译:使用自动车辆位置数据进行总线行程时间预测的节约方程的数值稳定性
机译:自动解释近似数值表达的尺寸:实证研究
机译:使用隐马尔可夫模型自动识别面部表情并估算表情强度。
机译:桉树术中近亲繁殖抑郁症的生命周期表达及其混合交配系统的跨代性稳定性
机译:问题赌博中的数字推理能力和非理性信念
机译:自动加农炮技术(aCT)计划。用配置参数变化确定弹性惯性矩和稳定性