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

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

Explanation:

Given the data in the question;

let us consider the approximate operation count for the system of n₁ equation in n₁ unknowns as;
`(2)/(3)n`₁³ Or

O₁ =
`(2)/(3)n`₁³

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

the appropriate operation count will be;

O₂ =
`(2)/(3)n`₂³

=
`(2)/(3)(3n_(1))`³

=
`(2)/(3)` × 27 × n₁³

= 27(
`(2)/(3)n`₁³ )

O₂ = 27(O₁)

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