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- Robert S. Anderssen, Markus Hegland
- Math. Comput.
- 1999

Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in… (More)

SUMMARY For the approximate solution of ill-posed inverse problems, the formulation of a regularization functional involves two separate decisions: the choice of the residual minimizer and the choice of the regularizor. In this paper, the Kullback–Leibler functional is used for both. The resulting regularization method can solve problems for which the… (More)

- Robert S. Anderssen, Frank R. de Hoog
- Computing
- 1984

In this paper, we derive results about the numerical performance of multi-point (moving average) finite difference formulas for the differentiation of non-exact data. In particular, we show that multi-point differentiators can be constructed which are asymptotically unbiased and have a bounded amplification factor as the steplength decreases and the number… (More)

- Robert S Anderssen, Peter M Waterhouse
- Methods in molecular biology
- 2012

The goal of this chapter is to describe in simple terms how the use of ordinary differential equation (ODE) modeling, in conjunction with experimentation, can be utilized to improve our understanding of the dynamics of gene silencing and virus resistance in plants.

- John W. Paine, Frank R. de Hoog, Robert S. Anderssen
- Computing
- 1981

The use of algebraic eigenvalues to approximate the eigenvalues of Sturm-Liouville operators is known to be satisfactory only when approximations to the fundamental and the first few harmonics are required. In this paper, we show how the asymptotic error associated with related but simpler Sturm-Liouville operators can be used to correct certain classes of… (More)

- M. Thamban Nair, Markus Hegland, Robert S. Anderssen
- Math. Comput.
- 1997

When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill–posed operator equations , assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for. In fact, it… (More)

- Frank R. de Hoog, Robert S. Anderssen
- Appl. Math. Lett.
- 2012

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis… (More)

In the modelling of genetic signalling, communication and switching (GSCS), there is a need to identify the various mechanistic models, which nature has discovered, in terms of simple positional information rules (Wolpert (1969a)). The discovery of such simple rules, however, is a highly non-trivial process; in part, because of the complexity of the… (More)