基于B-样条的Laplace积分算法研究(英文)

给出了 Laplace积分的 B-样条数值算法。采用三次样条函数的 B-样条矩阵表示 ,求其反问题 ,拟合 Laplace积分的象原函数。运用重节点技术描述象原函数的间断点 ,尖点和高阶不光滑点 ,再运用差商 ,de Boor递推算法 ,巧妙地导出了非均匀网格分划下 Laplace积分的象函数表达式 ,在准均匀网格分划下给出了一系列实用解析计算公式 ,大量算例具有良好的效果。计算机试验结果表明计算速度比用 Simpson方法要快得多 ,比传统方法——Berger方法要简单得多 ,克服了 Gauss-Laguerre积分 ,Gauss-Legendre积分函数零点 ,系数等难以确定的困难。解决了象原函数为超越函数的 Laplace积分象函数的计算问题。

AN NUMERICAL ALGORITHM FOR LAPLACE′S INTEGRAL BY B-SPLINE

Algorithm for Laplace′s integral is given when the inverse image function has high order discontinuity. The multi-node technique of B-spline is used to describe the interruption point, cusp and non-smooth point of the inverse image function. The difference quotient and de Boor algorithm are used to derive the image function of the Laplace′s integral under non-uniform partition. And a set of practical formula is got when the partition is quasi-uniform. The scheme enables the image function to be approximated within any prescribed tolerance. Experiments also show that good result is achieved. It is much faster than that of Simpsons rule, and much simpler than that of Berge method, the traditional efficient method. It is no longer to find the zero points and coefficients of Gauss-Laguerre or Gauss-Legendre polynomials. The image function of Laplace′s integral can also be computed while the inverse image function is hyper-function with high order discontinuity.