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Krylov Subspace Method

(efficient method of numerically solving sets of linear equations)

The Krylov Subspace Method is an Iterative Method of solving a set of Linear Equations that is efficient for computers, thus a preferred method of solving large sets of equations. It is iterative in that a series of approximations to the solution are produced, and using criteria to judge the closeness of the approximation to the solution, a trade-off can be made between accuracy and compute time.

It involves defining a Krylov Subspace for the Matrix representing the equations, by choosing a vector, and repeatedly multiplying the matrix to it.