Shown to the right is a set of log-log axes. The x-axis is the problem size N for a system of linear equations, and the y-axis is the total number of FLOPS to solve the system of equations. Directly on the axes, sketch the plots that show O(FLOPS) versus N for the following methods. Label each line accordingly. [3] a. Gauss Elimination. [LINE A] b. LU Decomposition, if L and U are already available for each system. [LINE B] c. Gauss-Seidel, assuming it takes = 100 iterations to converge regardless of N. [LINE C] log(FLOPS) 15 12 2 2 3 log(N)
Shown to the right is a set of log-log axes. The x-axis is the problem size N for a system of linear equations, and the y-axis is the total number of FLOPS to solve the system of equations. Directly on the axes, sketch the plots that show O(FLOPS) versus N for the following methods. Label each line accordingly. [3] a. Gauss Elimination. [LINE A] b. LU Decomposition, if L and U are already available for each system. [LINE B] c. Gauss-Seidel, assuming it takes = 100 iterations to converge regardless of N. [LINE C] log(FLOPS) 15 12 2 2 3 log(N)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![4. Shown to the right is a set of log-log axes. The x-axis is
the problem size N for a system of linear equations, and
the y-axis is the total number of FLOPS to solve the system
of equations. Directly on the axes, sketch the plots that
show (FLOPS) versus N for the following methods. Label
each line accordingly. [3]
a. Gauss Elimination. [LINE A]
b.
LU Decomposition, if I and U are already available
for each system. [LINE B]
Gauss-Seidel, assuming it takes i = 100 iterations
to converge regardless of N. [LINE C]
c.
log(FLOPS)
15
12
3
2
1
0
0
1
2
3
log(N)
4
5
Gauss Elimination →
Number of FLOPS
2n3
3
+ 9(n²)
Lu Decomposition → 0(n³) first solution
Ⓒ (n²) following
Gauss-Seidel → O(in²)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca6b5de9-d666-4be4-bec5-372f49facd74%2Fd27c38ac-96cd-4339-b5b3-c42eb772d60b%2Flbj2zci_processed.png&w=3840&q=75)
Transcribed Image Text:4. Shown to the right is a set of log-log axes. The x-axis is
the problem size N for a system of linear equations, and
the y-axis is the total number of FLOPS to solve the system
of equations. Directly on the axes, sketch the plots that
show (FLOPS) versus N for the following methods. Label
each line accordingly. [3]
a. Gauss Elimination. [LINE A]
b.
LU Decomposition, if I and U are already available
for each system. [LINE B]
Gauss-Seidel, assuming it takes i = 100 iterations
to converge regardless of N. [LINE C]
c.
log(FLOPS)
15
12
3
2
1
0
0
1
2
3
log(N)
4
5
Gauss Elimination →
Number of FLOPS
2n3
3
+ 9(n²)
Lu Decomposition → 0(n³) first solution
Ⓒ (n²) following
Gauss-Seidel → O(in²)
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