Question

use the approximate operation count 2n^3 /3 for guassian elimination to estimate how much longer it takes to solve n equations in n unknowns if n is tripled

Answer 1

Answer:

the appropriate operation count is 27 times longer than the original one.

Step-by-step explanation:

Given the data in the question;

let us consider the approximate operation count for the system of n₁ equation in n₁ unknowns as; $\frac{2}{3}n$₁³ Or  

O₁ =  $\frac{2}{3}n$₁³

so if the value of the unknowns is tripled i.e, n₂ = 3n₁,

the appropriate operation count will be;

O₂  =  $\frac{2}{3}n$₂³

= $\frac{2}{3}(3n_{1})$³

= $\frac{2}{3}$ × 27 × n₁³

= 27(  $\frac{2}{3}n$₁³  )

O₂ = 27(O₁)

Therefore, the appropriate operation count is 27 times longer than the original one.