EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 13, Problem 14P
Develop a program using a programming or macro language to implement the parabolic interpolation algorithm. Design the program so that it is expressly designed to locate a maximum and selects new points as in Example 13.2. The subroutine should have the following features:
• Base it on two initial guesses, and have the program generate the third initial value at the midpoint of the interval.
• Check whether the guesses bracket a maximum. If not, the subroutine should not implement the algorithm, but should return an error message.
• Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations.
• Return both the optimal x and
• Minimize the number of function evaluations.
Test your program with the same problem as Example 13.2.
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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.
6 108
polynomial is used to approximate v8, the answer is:
dy
13.
of the parametric equations x:
2-3t
3+2t
and y =-
is
dx
Use the following information for Questions 14 and 15:
1+t
1+t
Using the Newton-Raphson method to determine the critical co-ordinate of the graph
y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to
determine f'(x)
14.
The expression for f'(x) is:
The following tools were required in determining an expression for f'(x):
Application of the natural logarithm
15.
I.
II.
The product rule
III.
Implicit differentiation
Please help, this for Matlab the image is the first question with following 2 and 3 they go together.
2. Solving the question by using bisection.m with the stopping criterion at 1%. Report the root and # of iterations.
3. by using newton-Raphson matlab script with the stopping criterion at 0.1%. Report the root and # of iterations.
Chapter 13 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 13 - 13.1 Given the formula
(a) Determine the...Ch. 13 - 13.2 Given
(a) Plot the function.
(b) Use...Ch. 13 - Prob. 3PCh. 13 - Repeat Prob. 13.3, except use parabolic...Ch. 13 - 13.5 Repeat Prob. 13.3 but use Newton’s method....Ch. 13 - Employ the following methods to find the maximum...Ch. 13 - 13.7 Consider the following function:
Use...Ch. 13 - Employ the following methods to find the maximum...Ch. 13 - 13.9 Consider the following function:
Perform...Ch. 13 - Consider the following function:...
Ch. 13 - 13.11 Determine the minimum of the function from...Ch. 13 - Develop a program using a programming or macro...Ch. 13 - Develop a program as described in Prob. 13.12, but...Ch. 13 - 13.14 Develop a program using a programming or...Ch. 13 - 13.15 Develop a program using a programming or...Ch. 13 - Pressure measurements are taken at certain points...Ch. 13 - 13.17 The trajectory of a ball can be computed...Ch. 13 - 13.18 The deflection of a uniform beam subject to...Ch. 13 - An object with a mass of 100 kg is projected...Ch. 13 - The normal distribution is a bell-shaped curve...Ch. 13 - An object can be projected upward at a specified...Ch. 13 - Use the golden-section search to determine the...
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