FindRoot: Minimum Execution Time

Question

Is there a minimum execution time for the command FindRoot? If so, can I get rid of it?

For example, if I compute the time to solve the fundtion x=0, it takes around 0.27ms per evaluation:

In[581]:= AbsoluteTiming[Do[FindRoot[x, {x, 300}], {try, 1, 100}]]

Out[581]= {0.0270027, Null}

However, this is virtually the same time as it takes to solve a much more complex equation system {x=0,y=0,z=0}

In[580]:= AbsoluteTiming[Do[FindRoot[{x, y, z}, {{x, 300}, {y, 300}, {z, 300}}], {try, 1, 100}]]

Out[580]= {0.0280028, Null}

Since I am running findroot many times (the actual system is more complicated), I care about this "fixed" running cost. Is there a way to get rid of it?

Answer 1

AbsoluteTiming[Do[FindRoot[x, {x, 300}, Method -> "Secant"], {100}]]

Returns less than half the time of

AbsoluteTiming[Do[FindRoot[x, {x, 300}], {100}]]

Method, MaxIterations, and Jacobian are options that possibly have a faster alternative than "Automatic". If modifying these doesn't make it, you need to make your own findroot[] algorithm

If you use MachinePrecision, you should add Compiled -> True