Question: (a) Give an example of an interpolating polynomial through n + 1 points that has degree < n. (b) Can you explain, without referring to

(a) Give an example of an interpolating polynomial through n + 1 points that has degree < n.
(b) Can you explain, without referring to the explicit formulae, why all the Lagrange interpolating polynomials based on n + 1 points must have degree equal to n?

Step by Step Solution

★★★★★

3.40 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a For example the the interpolating polynomial for the data 0 0 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

952-M-L-A-E (2162).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Suppose an n ( (n + 1) matrix is row reduced to reduced echelon form. Approximately what fraction of the total number of operations (flops) is involved in the backward phase of the reduction when n =...

a. Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table: x f (x) 0.1 5.30000 0.0 2.00000 0.2 3.19000 0.3 1.00000 b....

a. Use Algorithm 3.2 to construct the interpolating polynomial of degree four for the unequally spaced points given in the following table: x f (x) 0.0 6.00000 0.1 5.89483 0.3 5.65014 0.6 5.17788 1.0...

1. Suppose you are constructing an interpolating polynomial for a function on an interval [a, b]. (a) (6 points) Explain under what circumstances and why you might want to use Chebyshev points to...

1. Describe what each assumption means to you and provide examples of each assumption. a. Development is multidimensional Aspects of our lives, such as intellectual, physical, and social, change in...

1456HHSC attend all (a) In the quantum teleportation protocol, Alice and Bob are every in possession of one qubit of a couple in the joint country00i + statei. Explain how the protocol works. In...

Describe, and estimate the costs of, procedures to (a) insert a new item into an existing heap; (b) delete the topmost item from a non-empty heap; (c) starting from an array holding N items in...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Math 104A Homework #2 Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made....

DETAILS What is the maximum segment length of a 100Base-FX netdwork, The last character ('X', etc) refers to the line code method used. Line code is a patdtern of voltage, current or photons used to...

Define the following accounting measurements and explain how and why they would be used when evaluating an entity: a. Working capital b. Current ratio c. Debt-to-equity ratio d. Gross margin e. Gross...

Write a C++ program to read user input of 10 integer numbers and stores them into an array and rearrange the array by moving all negative numbers to the front, without changing the original order of...

Question 1 KsTU Water Company has employed you as a consultant to undertake economic analysis of its proposed project to set up a factory in the Central Region to assess its viability before funds...

What is different from this case and a case in which property is taken for a freeway?

As indicated in the accompanying figure, let T: R2 R2 be the orthogonal projection on the line y = x (a) Find the kernel of T. (b) Is T one-to-one? Justify your conclusion. y y=x Tx)

Let be the matrix of T: P2 P2 with respect to the basis B = (v1, v2, v3), where v1 = 3x + 3x2, v2 = -1 + 3x + 2x2, v3 = 3 + 7x + 2x2. (a) Find [T(v1)]B, [T(v2)]B, and [T(v3)]B. (b) Find T(v1), T(v2),...

Let T1: P1 P2 be the linear transformation defined by T1(c0 + c1x) = 2c0 - 3c1x and let T2: P2 P3 be the linear transformation defined by T2(c0 + c1x + c2x2) = 3c0x + 3c1x2 + 3c2x3 Let B = (1, x),...

5 . Which statements describe the characteristics of the OSPF ( Open Shortest Path First ) protocol? OSPF _ _ _ _ _ _ _ _ . ( More than one statement applies ) .

You are considering buying some stock in GrowInc Company. You estimate that next year's dividend has the following probability distribution: You anticipate that next year's dividend will grow at a...

Your company took out an amortizing loan with the following terms: What is the annual payment on the loan (as a positive number)? Use Excel's PMT0 function. Attempt 1/10 for 10 pts. Create an...