Topics in matrix analysis
The complexity of robot motion planning
The complexity of robot motion planning
On the optimal stability of the Bernstein basis
Mathematics of Computation
Algebraic Geometry and Computer Vision: Polynomial Systems, Real andComplex Roots
Journal of Mathematical Imaging and Vision
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Applied Numerical Mathematics
Applied Numerical Mathematics
Ray-Tracing Polymorphic Multidomain Spectral/hp Elements for Isosurface Rendering
IEEE Transactions on Visualization and Computer Graphics
A unified approach to resultant matrices for Bernstein basis polynomials
Computer Aided Geometric Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
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Many problems in applied mathematics require the computation of the resultant of two polynomials, and it is nearly always assumed that the polynomials are expressed in the power basis. Recent work has shown that significantly improved numerical answers are obtained if the polynomials are expressed in the Bernstein basis, and thus the transformation of a resultant matrix between these bases is required. In this paper, this transformation is considered for one type of resultant, the companion matrix resultant. It is shown that this change of basis of the resultant matrix is defined by a similarity transformation, and that this transformation is ill-conditioned, even for matrices of low order. It is concluded that the companion matrix resultant should be constructed and computed in the Bernstein basis, such that the power basis is not used.