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

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.3: Matrix Approa To Solving Linear Systems
Problem 51PS
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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
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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