# linear, quadratic and cubic equations

• June 2nd, 2012, 03:18 PM
fatman57
linear, quadratic and cubic equations
I am studying computer science and have been covering linear, quadratic and cubic algorithms. I am confused as to the difference between them. Can someone explain what they mean in layman's terms?

Maybe even relate to physical objects? One possible example being that a cubic equation relates to three dimensions of something - so what does that mean in real terms that a computer has to go through (presumably in a linear fashion to compute the item) to come to a solution?

Make any sense?
• June 2nd, 2012, 05:04 PM
mathman
Usually these terms are used for polynomial equations where the highest power is 1 (linear), 2(quadratic), or 3 (cubic).

3 dimensions is something completely different.
• June 2nd, 2012, 05:27 PM
fatman57
Quote:

Usually these terms are used for polynomial equations where the highest power is 1 (linear), 2(quadratic), or 3 (cubic).

3 dimensions is something completely different.

thanks - could it simply be the fact that a quadratic represents a much larger number and is therfore a larger problem for a computer to solve than a linear one?
• June 3rd, 2012, 02:01 AM
wallaby
Quote:

thanks - could it simply be the fact that a quadratic represents a much larger number and is therfore a larger problem for a computer to solve than a linear one?

If we're talking about the "size" of a problem then my interpretation is that if you double the size of the input in a linear algorithm then the number of operations required to complete the task will also double, likewise if you triple the size of the input then 3 times as many operations will be performed. However if you double the size of the input in a quadratic algorithm then the algorithm will perform 4 times as many operations in calculating a solution. (tripling input will require 9 times as many operations) So we can see that if the algorithm is cubic then the run time will increase a lot when we start increasing the size of the problem even a little.
• June 3rd, 2012, 07:55 AM
fatman57
Quote:

Quote:

thanks - could it simply be the fact that a quadratic represents a much larger number and is therfore a larger problem for a computer to solve than a linear one?

If we're talking about the "size" of a problem then my interpretation is that if you double the size of the input in a linear algorithm then the number of operations required to complete the task will also double, likewise if you triple the size of the input then 3 times as many operations will be performed. However if you double the size of the input in a quadratic algorithm then the algorithm will perform 4 times as many operations in calculating a solution. (tripling input will require 9 times as many operations) So we can see that if the algorithm is cubic then the run time will increase a lot when we start increasing the size of the problem even a little.

ok - makes sense now - seems a silly question to ask really as cubic and quadratic problems are, well, exponentionally larger than a linear one! :P