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In computational mathematics, an iterative method attempts to solve a problem (for example an equation or system of equations) by finding successive approximations to the solution starting from an initial guess. This approach is in contrast to direct methods, which attempt to solve the problem in one-shot (like solving a linear system of equations Ax = b by finding the inverse of the matrix A). Iterative methods are useful for problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive and in some cases impossible even with the best available computing power.