3. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given bythe formula r;s(") for j 1,2, .n.= COS(2j-(a) Find an upper bound for the error for x E -1, 1] when the above Chebyshev nodes are usedto approximate f(r)erp(-4r?) with n = 6.The bound for error with 6 steps was found to be 7.0806e +05(b) Write a MATLAB code to interpolate f(x)[-1, 1] with n = 6. Make a plot showing the interpolation data, the exact function f(x), and thepolynomial interpolant. Make a second plot showing the error between the interpolant and f(x).How does the maximum error shown in this plot compare to your estimate?exp(-4r2) at the Chebyshev nodes for x E(c) Write a MATLAB code to interpolate f(r) = erp(-4r) at the Chebyshev nodes for x e -1,2] with n = 8. Make a plot showing the interpolation data, the exact function f(x), and thepolynomial interpolant. Make a second plot showing the error between the interpolant and f(x).

. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given by he formula r, = cos (E) for j= 1,2, ... n. a) Find an upper bound for the error for x E [-1, 1] when the above Chebyshev nodes are used o approximate f(r) = erp(-4r?) withn = 6. The bound for error with 6 stens was fouund to be 7 0806e-+05

. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given by he formula r, = cos (E) for j= 1,2, ... n. a) Find an upper bound for the error for x E [-1, 1] when the above Chebyshev nodes are used o approximate f(r) = erp(-4r?) withn = 6. The bound for error with 6 stens was fouund to be 7 0806e-+05

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.

Question

3. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given by
the formula r;
s(") for j 1,2, .n.
= COS
(2j-
(a) Find an upper bound for the error for x E -1, 1] when the above Chebyshev nodes are used
to approximate f(r)
erp(-4r?) with n = 6.
The bound for error with 6 steps was found to be 7.0806e +05
(b) Write a MATLAB code to interpolate f(x)
[-1, 1] with n = 6. Make a plot showing the interpolation data, the exact function f(x), and the
polynomial interpolant. Make a second plot showing the error between the interpolant and f(x).
How does the maximum error shown in this plot compare to your estimate?
exp(-4r2) at the Chebyshev nodes for x E
(c) Write a MATLAB code to interpolate f(r) = erp(-4r) at the Chebyshev nodes for x e -1,
2] with n = 8. Make a plot showing the interpolation data, the exact function f(x), and the
polynomial interpolant. Make a second plot showing the error between the interpolant and f(x).

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