### 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.

(*mathematics,computation*)
http://en.wikipedia.org/wiki/Krylov_subspace

http://www.sam.math.ethz.ch/~mhg/pub/biksm.pdf

http://meyer.math.ncsu.edu/Meyer/PS_Files/Krylov.pdf

**Referenced by:**

numerical analysis

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