Purpose of the methods
Krylov methods for solving linear systems

We are interested in the solution of linear systems Ax = b with hollow (i.e. with many zeros) non-singular matrices A of high dimension. Such systems must be solved, for example, when discretizing (systems of) partial differential equations by finite difference or finite element methods. The result is a linear system with a matrix containing few non-zero elements per row, for which it is useful to use special techniques to store only the non-zero elements of the matrix, and pointers that enable the row and column indices of the elements to be easily retrieved and the rows and/or columns to be traversed (see