There are many more matrix operations that actually exist: matrix exponential, matrix log, matrix trig functions, matrix square root, ...
E.g. exponential has an infinite series representation exp(x) = SUM_k x^k / k!: it works for matrices too, and is used
y = Mx
—>
x = M\y
Hamsters.js can also provide speedups, given you can translate your problem into a 'threaded' task.