General linear methods (GLMs) was introduced as a generalization of Runge{Kutta (RKMs) and multistep (LMMs). The discovery general method gave insight into the new that are neither RKMs or LMMs. Here, classes GLMs nested in their stages mono-implicit output presented, these referred to (NGLMs). Procedures for deriving members algebraically stable discussed herein NGLMs have been derived up orde...

MOTIVATION It is widely acknowledged that microarray data are subject to high noise levels and results are often platform dependent. Therefore, microarray experiments should be replicated several times and in several laboratories before the results can be relied upon. To make the best use of such extensive datasets, methods for microarray data fusion are required. Ideally, the fused data should...

The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error. In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investi...

We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p + 1. The results of numerical experiments confirm the reliability of these estimates. This research has applica...

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB T 1 + · · ·+ AKXB K = C. The most straightforward approach computes X ∈ Rm×n from the solution of an mn×mn linear system, typically limiting the feasible values of m,n to a few hundreds at most. Our new approach exploits the fact that X can often be well approximated by a low-rank matrix. It combines ...

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...

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