Question: The Chebyshev polynomials: (a) Prove that Tn(t) = cos(n arccos t), n = 0, 1, 2,... form a system of orthogonal polynomials under the weighted

The Chebyshev polynomials:
(a) Prove that
Tn(t) = cos(n arccos t), n = 0, 1, 2,...
form a system of orthogonal polynomials under the weighted inner product

(b) What is || Tn ||?
(c) Write out the formulae for T0(t),.... T6(t) and plot their graphs.

(f. g) = }-. rO8) d (5.62) - iVi- _ .

Step by Step Solution

★★★★★

3.44 Rating (179 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a To prove orthogonality use the change of variables t cos in the inner prod... 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 (2274).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

In this activity, you will get some practice with this tool by searching for specific procedure codes for evaluation and management codes (office visits) for codes 99201-99215. This activity will...

Prove that cos 2/x = 0. lim

Show that the Chebyshev polynomials have the following properties: (a) 2Tm(x)Tn(x) = Tm+n(x) + Tm-n(x), for m > n (b) Tm(Tn(x)) = Tmn(x)

Let Tn(x) denote the Chebyshev polynomial of degree n and define un-1(x) = 1/n Tn(x) If x = cos , show that U-1Cx)sin n Un-x)Sinn sin

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Find the eigenvalues and eigenfunctions. Verify orthogonality. Start by writing the ODE in the form (1), using Prob. 6. Show details of your work. Orthogonal polynomials play a great role in...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

7:50 P Q 14 .Ill 37% chegg.com/homework-help 2 . . . s] Given the matrix 1 2 A = 3 6 5 10 determine all four subspaces RA, NA, RAt, NA+. 4 19 Find the least squares approximation b to the vector b =...

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

Math 400 Assignment #3 -- Numerical Integration and Differentiation 1. For the function g x e x 2 2 Due: 6am April 09, 2016 use the centered difference formula with h 101 , 102 , , 1020 to create a...

World- famous mining mogul Steve Wilsey hired the public accounting firm of Joe Wang Associates, PC, to conduct an audit of his new acquisition, Cougar Goldust, Inc. The gold inventory was scheduled...

a. The average person doesnt like working the night shift. According to the theory of compensating differentials, are night shift wages probably higher or lower than day shift wages? b. Most...

determine the transformed cross - section in positive bending for the following composite cross - section

Ebba Co. is experiencing a decrease in sales and operating income for the fiscal year ending December 31, 2010. Cody Bryant, controller of Ebba Co., has suggested that all orders received before the...

Calculate the magnitude and direction of the net gravitational force on the moon due to the earth and the sun when the moon is in each of the positions shown in Fig. 12.32. (Note that the figure is...

Adams Corporation is considering four average-risk projects with the following costs and rates of return: The company estimates that it can issue debt at a rate of r d = 10%, and its tax rate is 30%....

At the end of every year NIKE and adidas record inventory write-downs for items (footwear and apparel) that have lost value due to a variety of reasons, such as changing styles, defective...

The circuit in Figure P26.38 consists of two identical parallel metal plates connected by identical metal springs to a 100-V battery. With the switch open, the plates are uncharged, are separated by...

What is the meaning of economizing of resources?

Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The time until a projectile returns to earth. (b) The number of times a transistor...

In circuit testing of printed circuit boards, each board either fails or does not fail the test. A board that fails the test is then checked further to determine which one of five defect types is the...

The data from 200 machined parts are summarized as follows: Depth of bore Above Below Edge condition Target Target Coarse 15 10 Moderate 25 20 Smooth 50 80 (a) What is the probability that a part...

at an interest rate of 11 percent. Click the icon to view the table of or discrete compounding periods when i=11%. The savings would need to be at least $30170.6. (Round to the nearest cent as...

Mary Reid works as a financial advisor at Wells Fargo Wealth Management team. She is a big believer of the capital asset pricing model and often use it for making recommendations to her clients. One...

Three cards are dealt to the player. What are the chances of not receiving three hearts?