Matrix-free methods

In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products. Such methods can be preferable when the matrix is so big that storing and manipulating it would cost a lot of memory and computer time, even with the use of methods for sparse matrices. Many iterative methods allow for a matrix-free implementation, including the power method and the conjugate gradient method.

References

• Langville, Amy N.; Meyer, Carl D. (2006), Google's PageRank and beyond: the science of search engine rankings, Princeton University Press, p. 40, ISBN 978-0-691-12202-1.