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 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. http://www.sam.math.ethz.ch/~mhg/pub/biksm.pdf http://meyer.math.ncsu.edu/Meyer/PS_Files/Krylov.pdf |