Chapter 3 Interpolation - MIT OpenCourseWare
https://ocw.mit.edu/courses/18-330-introduction-to-numerical-analysis-spring-2012/fd3b0e48e1babfcc36db7c012078318d_MIT18_330S12_Chapter3.pdf
WEB1That's because, if we x j, we can divide Lk(x) by (x xj), j = 6 k. We obtain Lk(x) = (x xj)q(x) + r(x), where r(x) is a remainder of lower order than x xj, i.e., a constant. Since Lk(xj) = 0 we must have r(x) = 0. Hence (x xj) must be a factor of Lk(x). The same is true of any (x xj) for j …
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