Homework
, Math 104 A
1
Instructor: Prof. Hector D. Ceniceros
General Instructions
: You have to integrate all the problems that require coding and/or
numerical computation in a single jupyter notebook. Make sure
all your codes
have a pream-
ble which describes purpose of the code, all the input variables, the expected output, your
name, and the date of the last time you modified it. Write your own code, individually. Do
not copy codes! The solutions to the problems that do not require coding must be uploaded
as a single pdf or as part of the jupyter notebook.
1. (a) Equating the leading coefficient of the Lagrange form of the interpolation polyno-mialpn(x) with that of the Newton’s form deduce thatf[x0, x1, . . . , xn] =nXj=0f(xj)nQk=0k6=j(xj-xk).(1)(b) Use (1) to conclude that divided differences are symmetric functions of their argu-ments, i.e. any permutation ofx0, x1, . . . , xnleaves the corresponding divided differenceunchanged.2. In Newton’s form of the interpolation polynomial we need to compute the coefficients,c0=