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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 2n 2n 2n /3+0(n2) n/3+0(n²) Matrix-vector multiplication LU factorization Cholesky factorization Back/forward substitution Tridiagonal solve 8 You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider then by n linear system Aa b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutos. 2.75 E7 O1.04E5 O 1.31E5 9.45E13

The computational complexities of some common operations with n by n matrices are given in the table below. Operations Matrix-matrix multiplication Flops 2n 2n 2n /3+0(n2) n/3+0(n²) Matrix-vector multiplication LU factorization Cholesky factorization Back/forward substitution Tridiagonal solve 8 You have a 2.5 GHz workstation with 6 cores where each core can do 6 floating point operations per clock cycle. Consider then by n linear system Aa b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutos. 2.75 E7 O1.04E5 O 1.31E5 9.45E13

Advanced Engineering Mathematics
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 Matrix-vector multiplication LU factorization Cholesky factorization Back/forward substitution Tridiagonal solve Flops 2n 2n 2n/3+ 0(n?) n/3+0(n²) 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 Az b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutos. O 2.75E7 1.04E5 1.31 E5 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 Matrix-vector multiplication LU factorization Cholesky factorization Back/forward substitution Tridiagonal solve Flops 2n 2n 2n/3+ 0(n?) n/3+0(n²) 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 Az b where A is tridiagonal. Estimate the largest value of n such that the linear system can be solved in 140 minutos. O 2.75E7 1.04E5 1.31 E5 9.45E13
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