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1. Write a function lagrange_poly which computes the kth Lagrange basis polynomial. It should take as arguments an array of points x, the list of interpolation points xk, and an integer k, and return an array of numbers Lk (x) according to (3.1). 2. Write a function interpolating_poly which computes the Lagrange interpolating polynomial given by (3.2). It should take as arguments an array of points z and lists of data points and fk, and call the function lagrange_poly when necessary.

1. Write a function lagrange_poly which computes the kth Lagrange basis polynomial. It should take as arguments an array of points x, the list of interpolation points xk, and an integer k, and return an array of numbers Lk (x) according to (3.1). 2. Write a function interpolating_poly which computes the Lagrange interpolating polynomial given by (3.2). It should take as arguments an array of points z and lists of data points and fk, and call the function lagrange_poly when necessary.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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3.2.2.1 Lagrange interpolation The principles of Lagrange interpolation were introduced in the lecture. Recall that this takes a set of n +1 data points, (æk, fk) with k = 0,..., n, and defines Lagrange basis polynomials by Lk(x) = n II 20 i=0 i#k T-Ti Thi k = 0,..., n. The Lagrange interpolating polynomial is then defined by n P(x) = Σ fkLk (x). k=0 (3.1) (3.2) Note that, for convenience in Python, indices in equations (3.1) and (3.2) start at 0. There are n+ 1 interpolation points and P(x) is therefore of degree n. CHAPTER 3. INTERPOLATION 1. Write a function lagrange_poly which computes the kth Lagrange basis polynomial. It should take as arguments an array of points x, the list of interpolation points xk, and an integer k, and return an array of numbers L(x) according to (3.1). 2. Write a function interpolating_poly which computes the Lagrange interpolating polynomial given by (3.2). It should take as arguments an array of points x and lists of data points k and fk, and call the function lagrange_poly when necessary.
Transcribed Image Text:3.2.2.1 Lagrange interpolation The principles of Lagrange interpolation were introduced in the lecture. Recall that this takes a set of n +1 data points, (æk, fk) with k = 0,..., n, and defines Lagrange basis polynomials by Lk(x) = n II 20 i=0 i#k T-Ti Thi k = 0,..., n. The Lagrange interpolating polynomial is then defined by n P(x) = Σ fkLk (x). k=0 (3.1) (3.2) Note that, for convenience in Python, indices in equations (3.1) and (3.2) start at 0. There are n+ 1 interpolation points and P(x) is therefore of degree n. CHAPTER 3. INTERPOLATION 1. Write a function lagrange_poly which computes the kth Lagrange basis polynomial. It should take as arguments an array of points x, the list of interpolation points xk, and an integer k, and return an array of numbers L(x) according to (3.1). 2. Write a function interpolating_poly which computes the Lagrange interpolating polynomial given by (3.2). It should take as arguments an array of points x and lists of data points k and fk, and call the function lagrange_poly when necessary.
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