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- Elena Celledoni, Arne Marthinsen, Brynjulf Owren
- Future Generation Comp. Syst.
- 2003

RKMK methods and Crouch-Grossman methods are two classes of Lie group methods. The former is using flows and commutators of a Lie algebra of vector fields as a part of the method definition. Theâ€¦ (More)

- Menno Lodder, W. F. Lems, +6 authors J. C. Roos
- Annals of the rheumatic diseases
- 2004

BACKGROUND
Bone mineral density (BMD) measurements are frequently performed repeatedly for each patient. Subsequent BMD measurements allow reproducibility to be assessed.
OBJECTIVE
To examine theâ€¦ (More)

- Brynjulf Owren, Arne Marthinsen
- Numerische Mathematik
- 2001

We present a new class of integration methods for di erential equations on manifolds, in the framework of Lie group actions. Canonical coordinates of the second kind is used for representing the Lieâ€¦ (More)

Integration of Lie type equations on matrix Lie groups using Magnus series methods has recently been proposed by Iserles and N rsett. The methods use the exponential mapping, whose computation may beâ€¦ (More)

- Zdzislaw Jackiewicz, Arne Marthinsen, Brynjulf Owren
- Adv. Comput. Math.
- 2000

An approach is described to the numerical solution of order conditions for RungeKutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization usingâ€¦ (More)

- Arieh Iserles, Arne Marthinsen, S. P. N rsett
- 1998

The method of Magnus series has recently been analysed by Iserles & N rsett (1997). It approximates the solution of linear di erential equations y = a(t)y in the form y(t) = e , solving a nonlinearâ€¦ (More)

During the last few years, di erent approaches for integrating ordinary di erential equations on manifolds have been published. In this work, we consider two of these approaches. We present someâ€¦ (More)

- Arne Marthinsen
- SIAM J. Numerical Analysis
- 1999

We consider interpolation in Lie groups. Based on points on the manifold together with tangent vectors at (some of) these points, we construct Hermite interpolation polynomials. If the points andâ€¦ (More)

This paper presents a family of generalized multistep methods that evolves the numerical solution of ordinary di erential equations on con guration spaces formulated as homogeneous manifolds. Anyâ€¦ (More)

- Arne Marthinsen, Arne Marthinseny
- 1998

We consider interpolation in Lie groups and homogeneous spaces. Based on points on the manifold together with tangent vectors at (some of) these points, we construct Hermite interpolationâ€¦ (More)