The computational complexities of some common operations

Last updated: 6/23/2023

The computational complexities of some common operations with 12 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 0 027 seconds 7 4E 6 seconds 4 3 minutes 8 7 minutes Flops 2n 3 2n 2n 3 0 n n 3 0 n You have a 2 6 GHz workstation with 6 cores where each core can do 2 floating point operations per clock cycle Estimate how long it will take to solve the n by n linear system Ax b where A is upper triangular and n 28 997 72 8n You have a 2 6 GHz workstation with 6 cores where each core can do 2 floating point operations per clock cycle Estimate how long it will take to solve the n by n linear system Ax b where A is upper triangular and n 28 997