1. A method comprising: training a deep neural network, wherein the training comprises: receiving and formatting speech data for the training, wherein the speech data is received from a speech data collector; preconditioning a system of equations to be used for analyzing the formatted speech data in connection with the training by using a non-fixed point quasi-Newton preconditioning scheme; generating at least one solution based on the preconditioned system of equations, wherein generating the at least one solution comprises employing flexible Krylov subspace solvers in response to variations in the preconditioning scheme for different iterations of the training; and communicating the at least one solution to the deep neural network; wherein the receiving, formatting, preconditioning, generating and communicating steps are performed by a computer system comprising a memory and at least one processor coupled to the memory.