Hu Xu-Guang, Ho Tak-San, Rabitz Herschel
Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):035701. doi: 10.1103/PhysRevE.65.035701. Epub 2002 Mar 6.
Accurate and efficient rational approximation schemes are presented for interpolating multidimensional scattered data with a novel weighted least-squares procedure including domain decomposition. Two particular representations of the method are formulated and the corresponding algorithms are implemented. Numerical tests on three- and six-dimensional model systems are carried out, demonstrating high efficiency and accuracy. This work was motivated by the need for multidimensional function approximation using irregular grids when solving quantum fluid dynamics equations, and the method should have broader physical applications.
提出了精确且高效的有理逼近方案，用于通过一种包括区域分解的新型加权最小二乘法对多维散射数据进行插值。阐述了该方法的两种具体表示形式，并实现了相应算法。对三维和六维模型系统进行了数值测试，结果表明该方法具有高效性和准确性。这项工作是受求解量子流体动力学方程时使用不规则网格进行多维函数逼近的需求所推动，并且该方法应具有更广泛的物理应用。
