首都师范大学学报（自然科学版）2011，Vol.32Issue(5)：7-10,4.
切比雪夫的最小二乘法插值理论研究
Chebyshev's Interpolation Theory by the Method of Least Squares
摘要
Abstract
Based upon systematically analyzing the work of P. L. Chebyshev, this paper discusses Chebyshev ' s significant contribution to interpolation by the method of least squares. Chebyshev first develop the general theory about "interpolation by the method of least squares" and later treads the special case of equidistant arguments. He requires of the approximating polynomial that it minimize the sum of the squared residuals. His method of solving the normal eqution leads him to write the orthogonal polynomial as a linear combination of a set of polynomials which he proves to be orthogonal. The least squares fitting of polynomial of increasing degree to data, whether equidistant or not, by means of orthogonal polynomial is thus fully developed by Chebyshev.关键词
切比雪夫/正交多项式/最小二乘法/等距变量Key words
P.L.Chebyshev/orthogonal polynomial/the method of least squares/equidistant arguments分类
自科综合引用本文复制引用
徐传胜,白欣..切比雪夫的最小二乘法插值理论研究[J].首都师范大学学报（自然科学版）,2011,32(5):7-10,4.基金项目
国家自然科学基金(10771169) （10771169）
教育部人文社科项目(10YJA720035). （10YJA720035）
