Could markets compute equilibria? It has been shown, for example in the papers


Deng, Du, The Computation of Approximate Competitive Equilibrium is PPAD-hard
Hirsch, Papadimitriou, Vavasis, Exponential Lower Bounds for Finding Brouwer Fixed Points


that finding competitive equilibria is in a certain sense computationally intractable.
So how does economic theory expect a market to reach a competitive equilibrium if each agent is presumably representable by an efficient computational process?
In fact, parallel computation doesn't really help because a polynomial number of processors can be simulated in polynomial time.
Computing an equilibrium is not needed for implementing it. This was the mistake of Lange and co. and was decisively rebutted by Hayek.
If you want a mathematical formulation, simply take a tatonement process. Given prices, each individual needs to compute her net demand correspondence. Under different tatonement mechanisms, which are an idealization of the dynamic process of price adjustment in the real-world economy, prices should converge to approximate equilibria. In both experimental settings and in financial markets, there is ample evidence for convergence.