Class RealLinearOperator

  • Direct Known Subclasses:
    AbstractRealMatrix, JacobiPreconditioner

    public abstract class RealLinearOperator
    extends Object
    This class defines a linear operator operating on real (double) vector spaces. No direct access to the coefficients of the underlying matrix is provided. The motivation for such an interface is well stated by Barrett et al. (1994):
    We restrict ourselves to iterative methods, which work by repeatedly improving an approximate solution until it is accurate enough. These methods access the coefficient matrix A of the linear system only via the matrix-vector product y = A · x (and perhaps z = AT · x). Thus the user need only supply a subroutine for computing y (and perhaps z) given x, which permits full exploitation of the sparsity or other special structure of A.

    Barret et al. (1994)
    R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM