Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Let f(x) = 2x3 − 11.7x2 + 17.7x − 5. Use Fixed-point iteration method startingwith the initial guess x0 = 3 to find the root of f(x). Perform 3 iterations. Carry sixdecimal places in all calculations.
find a bound for the number of iterations needed to achieve an approximation with accuracy 10−3 to the solution of 2x 6 − 5x 4 + 2 = 0 in the interval [0, 1] while using the bisection method
Find the root of the function:
f(x) = x^5 + 2x^4 − 3x^3 + 4x^2 − 5x + 6
using Regula Falsi Method with initial conditions xL=−4 and xU=−3.Perform up to 5 iterations.
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- Solve this problem with the Jacobi's iteration method to ea = 5%.arrow_forwardFind the fourth iteration value of z using the Gauss-Seidel method with an initial guess of (1, 1, 3). Round off your final answer to nine decimal places. Do not round off in preliminary calculations.arrow_forwardDetermine the positive real root of ln(x2)=0.7 a. graphically b. using three iterations of the bisection method, with initial guesses of xl=0.5 and xu=2 c. using three iterations of the false position method, with the same initial guesses of xl=0.5 and xu=2arrow_forward
- Find a successive approximation of the square root of 2 as a ratio of two integers by using the Newton –Raphson method analytically. Use the 1 as a starting point and provide at least 10 iterations.arrow_forward1. Use the Fixed-point iteration method and Bisection Method to findsolutions to within 10^-4 x^3 + 2x^2 – 5 = 0, [1, 4]arrow_forwardCarry out the five iterations of by using bisection method. F(x)=xcosx-2x^2+3x-1 0<=x<=1arrow_forward
- SHOW ONLY THE FORMULA TO GET THE ITERATIONS IN EXCEL USING THE METHOD GIVENarrow_forwardFind values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions.arrow_forward3. The function f(x) = xe=^(-x) has a unique root x = 0.(a) Compute several iterations of the Newton's method, and conclude that the methoddoes not succeed if x_0 > 1.(b) Draw graphs to illustrate the rst few iteration when x_0 = 0.5 and x_0 = 1.5.arrow_forward
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