High Quality Content by WIKIPEDIA articles! In mathematics, preconditioning is a procedure of an application of a transformation, called the preconditioner, that conditions a given problem into a form, which is more suitable for numerical solution. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. The most common use of preconditioning is for iterative solution of linear systems resulting from approximations of partial differential equations. In this application, both the matrix A and the preconditioner P depend on the mesh-size parameter, traditionally denoted by h. In such a case, the goal of optimal preconditioning is, on the one side, to make the spectral condition number of P ? 1A to be bounded from above by a constant independent in h, which is called spectrally equivalent preconditioning by D'yakonov.

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