  New iterative methods for solving linear equations are presented that are
easy to use, generalize good existing methods, and appear to be faster. The new
algorithms mix two kinds of linear recurrence formulas. Older methods have
either high order recurrence formulas with scalars for coefficients, as in
truncated orthomin, or have 1st order recurrence formulas with matrix
polynomials for coefficients, as in restarted gcr/gmres. The new methods
include both: high order recurrence formulas and matrix polynomials for
coefficients. These methods provide a trade-off between recurrence order and
polynomial degree that can be exploited to achieve greater efficiency.
Convergence results are obtained for both constant coefficient and varying
coefficient methods.

Numerical Analysis