You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider the n by n linear system Ax = b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutes. O 2.75E7 1.04E5 O 1.31E5 9.45E13
You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider the n by n linear system Ax = b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutes. O 2.75E7 1.04E5 O 1.31E5 9.45E13
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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![The computational complexities of some common operations with n by n matrices are given in the table below.
Operations
Matrix-matrix multiplication
Flops
2n3
Matrix-vector multiplication
2n2
2n /3 + O(n²)
n3 /3 + O(n²)
LU factorization
Cholesky factorization
Back/forward substitution
n2
Tridiagonal solve
8n
You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider the n
by n linear system Ax
140 minutes.
b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in
||
2.75E7
1.04E5
1.31E5
9.45E13](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2646376f-cb50-4931-8364-53b7ffbaab87%2F02df12bf-5b4d-4fbd-982a-d0f00aa12fb3%2Fhcxo4k9_processed.png&w=3840&q=75)
Transcribed Image Text:The computational complexities of some common operations with n by n matrices are given in the table below.
Operations
Matrix-matrix multiplication
Flops
2n3
Matrix-vector multiplication
2n2
2n /3 + O(n²)
n3 /3 + O(n²)
LU factorization
Cholesky factorization
Back/forward substitution
n2
Tridiagonal solve
8n
You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider the n
by n linear system Ax
140 minutes.
b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in
||
2.75E7
1.04E5
1.31E5
9.45E13
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