On condition numbers and algorithms for determining a rigid body movement

• Using a set of landmarks to represent a rigid body, a rotation of the body can be determined in the least-squares sense as the solution of an orthogonal Procrustes problem. We discuss some geometrical properties of the condition number for the problem of determining the orthogonal matrix representing the rotation. It is shown that the condition number depends critically on the configuration of the landmarks. The problem is also reformulated as an unconstrained nonlinear least-squares problem and the condition number is related to the geometry of such problems. In the common 3-D case, the movement can be represented by using a screw axis. Also the condition numbers for the problem of determining the screw axis representation are shown to depend closely on the configuration of the landmarks. The condition numbers are finally used to show that the algorithms used are stable.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

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Scientific Computing

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