EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 5, Problem 22P
Develop a subprogram for the bisection method that minimizes function evaluations based on the pseudocode from Fig. 5.11.
Determine the number of function evaluations
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We have designed a divide-and-conquer algorithm that runs on an input of size n. This algorithm works by spending O(1) time splitting the problem in half, then does a recursive call on each half, then spends O(n2 ) time combining the solutions to the recursive calls. On small inputs, the algorithm takes a constant amount of time. We want to see how long this algorithm takes, in terms of n to perform the task.
(a) First, write a recurrence relation that corresponds to the time-complexity of the above divide and conquer algorithm.
(b) Then, solve the relation to come with the worst-case time taken for the algorithm.
Please show all work in depth.
Problem 6.5
f(x)=-0.9x? +1.7x+2.5 Calculate the root of the
function given below: a) by Newton-Raphson
method b) by simple fixed-point iteration
method. (f(x)=0) Use x, = 5 as the starting
value for both methods. Use the approximate
relative error criterion of 0.1% to stop
iterations.
Chapter 5 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 5 - 5.1 Determine the real roots...Ch. 5 - 5.2 Determine the real root of:
(a) Graphically....Ch. 5 - 5.3 Determine the real root of:
(a)...Ch. 5 - Determine the roots of f(x)=1221x+18x22.75x3...Ch. 5 - Locate the first nontrivial root of sin x=x2wherex...Ch. 5 - 5.6 Determine the positive real root of (a)...Ch. 5 - 5.7 Determine the real root of:...Ch. 5 - 5.8 Find the positive square root of 18 using the...Ch. 5 - 5.9 Find the smallest positive root of the...Ch. 5 - 5.10 Find the positive real root of using the...
Ch. 5 - 5.11 Determine the real root of: (a) analytically...Ch. 5 - 5.12 Given
Use bisection to determine the...Ch. 5 - 5.13 The velocity v of a falling parachutist is...Ch. 5 - 5.14 Use bisection to determine the drag...Ch. 5 - As depicted in Fig. P5.15, the velocity of water,...Ch. 5 - 5.16 Water is flowing in a trapezoidal channel at...Ch. 5 - 5.17 You are designing a spherical tank (Fig....Ch. 5 - The saturation concentration of dissolved oxygen...Ch. 5 - 5.19 According to Archimedes principle, the...Ch. 5 - 5.20 Perform the same computation as in Prob....Ch. 5 - 5.21 Integrate the algorithm outlined in Fig. 5.10...Ch. 5 - Develop a subprogram for the bisection method that...Ch. 5 - 5.23 Develop a user-friendly program for the...Ch. 5 - Develop a subprogram for the false-position method...Ch. 5 - 5.25 Develop a user-friendly subprogram for the...Ch. 5 - 5.26 Develop a function for bisection in a similar...
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