Solving a cubic equation

Hi,

I have the following equation to solve

Z^3 - (1-B)Z^2 + Z(A-3B-2B^2) - (AB-B^2-B^3)

A and B are vectors. Can the solve function be used to output the roots in an nx3 matrix?

Answer 1

[Matt J]

I would just use ROOTS in a loop.

Answer 2

[John D'Errico]

As Matt says, roots in a loop will work. Often the simplest is best, as why expend programming time on something so simple.

If you really want it to be vectorized, you COULD convert the array into a cell array. The use cellfun, with @roots to solve all the problems at once.

If you REALLY want it vectorized and fast as blazes, then since this is a cubic polynomial, use the classic solution for the roots of a cubic given the coefficients. That formula can be used in a vectorized form. Trivial really. This is in fact what we did when we had to solve that same problem, and we wanted pure speed.