(2.3.1)--Chapter2-2.3-NewtonMethodforInte冷热源工程冷热源工程.ppt

2.3 The Newton polynomial interpolation Method(1) 2.3.1 The Newton polynomial interpolation MethodLagrange interpolation method needs to recalculate all basis functions when adding nodes, so the method is not inherited. From linear algebra we know that any polynomial whose degree is equal to or less than n can be expressed as a linear combination of the following functions:This form is called Newton polynomial, denoted as that is, Thus, a polynomial interpolation of degree n can be expressed as a Newton Newton interpolation methodWe call the Newton polymodal of degree n that satisfies the interpolationcondition as the Newton interpolation polynomial whose coefficients are to be determined???Newton interpolation method transforms the polynomial interpolation problem from solving a system of equations of (n + 1) dimension to simple (n+1) equations of only one variable. How to find out the patterns of the coefficients of the Newton interpolation polynomial so that we can solve them efficiently using computers? ？ 2.3 The Newton polynomial interpolation Method (1) Popup Questions： 1. The interpolation basis function of the Newton interpolation method is both node-related and power-increasing, which improves the Lagrange interpolation method that lacks the inheritance. right? (Correct)2. If we change the order of interpolation nodes, the basis functions of the Lagrange interpolation and the Newton interpolation will be (c)b. changed, same;c. same, changed;a. both changed; d. same, same;