EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 11, Problem 7P
Compute the Cholesky decomposition of
Do your results make sense in terms of Eqs.
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Students have asked these similar questions
1. Consider the following square matrix
A =
9 6
(a) Determine the eigenvalues and eigenvector(s) of A.
(b) Find the modal matrix M and diagonalize A through similarity transformation M 'AM.
do we get a Jordan form or not? Explain why?
Suppose that the stiffness matrices of the above question (as shown below) are as
follows:
b -b
a
a
K1 =108 x
K2 =108 x
-b
-a
a
b
0.1 m
0.05 m
0.5 m
0.5 m
where a= 1.8 N/m and b=2.9 N/m. Find the assembled stiffness matrix of the system
using the following connectivity table.
Element Node i Node j
(1)
2
(2)
2
What is the summation of all terms located on the main diagonal of the assembled
[a bc]
stiffness matrix? (Hint: if the assembled stiffness matrix is
b de
then you
e f
need to find the value of a + d+ f).
Your Answer:
Answer
The shape function value
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O is always higher than 1.
O is equal 1 at its own node and zero at other nodes.
O is always less than 1.
Suppose that three coordinate frames 0₁X1Y1Z1, 02X2V2Z2 and 03X3Y3Z3 are given, and
0]: P².
p³
1
0
R3 = 0 0.5
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0.866
Find p¹ and matrix R₂.
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Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 11 - 11.1 Perform the same calculations as in (a)...Ch. 11 - Determine the matrix inverse for Example 11.1...Ch. 11 - 11.3 The following tridiagonal system must be...Ch. 11 - 11.4 Confirm the validity of the Cholesky...Ch. 11 - Perform the same calculations as in Example 11.2,...Ch. 11 - Perform a Cholesky decomposition of the following...Ch. 11 - Compute the Cholesky decomposition of...Ch. 11 - Use the Gauss-Seidel method to solve the...Ch. 11 - Recall from Prob. 10.8, that the following system...Ch. 11 - 11.10 Repeat Prob. 11.9, but use Jacobi...
Ch. 11 - 11.11 Use the Gauss-Seidel method to solve the...Ch. 11 - Use the Gauss-Seidel method (a) without relaxation...Ch. 11 - 11.13 Use the Gauss-Seidel method (a) without...Ch. 11 - Redraw Fig. 11.5 for the case where the slopes of...Ch. 11 - 11.15 Of the following three sets of linear...Ch. 11 - Use the software package of your choice to obtain...Ch. 11 - Given the pair of nonlinear simultaneous...Ch. 11 - An electronics company produces transistors,...Ch. 11 - Use MATLAB or Mathcad software to determine the...Ch. 11 - Repeat Prob. 11.19. but for the case of a...Ch. 11 - 11.21 Given a square matrix , write a single line...Ch. 11 - Write the following set of equations in matrix...Ch. 11 - In Sec. 9.2.1, we determined the number of...Ch. 11 - 11.24 Develop a user-friendly program in either a...Ch. 11 - 11.25 Develop a user-friendly program in either a...Ch. 11 - Develop a user-friendly program in either a...Ch. 11 - As described in Sec. PT3.1.2, linear algebraic...Ch. 11 - A pentadiagonal system with a bandwidth of five...
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