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

See similar textbooks

Similar questions

(1) (a) Show that n(n² – 1)(n + 2) is divisible by 4 for all integer n. (b) Prove by contradiction : if n – m is odd , then n2 – m? is odd .
2. Show that each of the following formulas are both satisfiable and falsifiable. (a) y Vxp(x, y). (b) Vr (p(x) V q(x)) → (Vxp(x)) v (Vxq(x)) (c) Vx (yp(x,y) →yq(x, y)).
Let Express in terms of 1 A = [₂ 2 and 2-² = [2] Α B-¹ 3 and find all its entries. ((BA)T)-¹ A and B-¹
If X~ N(3,9), find (a) Pr(2 0) (c) Pr(|X3|> 6).
Please help with this question!
Consider the function f(x) = 1 3x+1 . We approximate f(x) by the Lagrange interpolating polynomial P₂ (x) at the points xo = 1, x₁ = 1.5 and.x₂ = 2. A bound of the theoretical error of this approximation at x = 1.8 is:
Using MATLAB functions poly and polyder, compute the relative condition numbers of the roots 1, 2, ..., 20 of the Wilkinson polynomial 20 w(x) = (x1)(x-2)(x - 20) = x²0 210x¹⁹+... 19 with respect to perturbation of the coefficient of 2x¹⁹, a19, from -210 to -210+2-23 Present your results in a tabular form and write your conclusion on the ill-conditioninig of the Wilkinson polynomial. (Recall: condition number for the jth root is kj |a₁x²=1| \w'(x₂)
QUESTION 14 In a bisection method, after applying one iteration, by how much did our interval that might contain a zero of f(x) decrease? 15% 25% 50% 75% Gauss Method None of the answers
A. Problem Solving (Bracketing Method): Solve the following problem using Bisection Method and False Position Method. Using the format below for your answer tabulation: N XI Xu Xr Ea Et f(x)f(xr)
Question 3 In 12–17, use the IVT to verify each function has a root in the given interval(s). Then use the Bisection Algorithm to narrow the location of that root to an interval of length less than or equal to 0.1. f(x) = x^2 − 2 on [0, 3] Full explain this question and text typing work only thanks
Theorem 1 (Master Theorem). Let a ≥ 1 and b> 1 be constants, let f(n) be a function f: N→ R+, and let T(n) be defined on the nonnegative integers by the recurrence T(n)= aT(n/b) + f(n). Then T(n) has the following asymptotic bounds: 1. if f(n) = O(nlogs a-E) for some constant e > 0, then T(n) = (nossa), 2. if f(n) = (nlos a) then T(n) = (nloga log n), and 3. if f(n) = N(n¹og a+s) for some e > 0 and if af (n/b) ≤df (n) for some constant d < 1 and all sufficiently large n, then T(n) = (f(n)). Use the Master Theorem above to solve the following recurrences when possible (note that not every blank needs to be filled in in every problem):
Use the Python code for Gauss-Seidel method to solve problem 11.13 to a tolerance of ε s=10^-10. i need code as well.