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Foundations of Computational Mathematics
Published in: Foundations of Computational Mathematics 3/2013

01-06-2013

Subdivision Schemes for Positive Definite Matrices

Authors: Uri Itai, Nir Sharon

Published in: Foundations of Computational Mathematics | Issue 3/2013

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Abstract

The class of symmetric positive definite matrices is an important class both in theory and application. Although this class is well studied, little is known about how to efficiently interpolate such data within the class.
We extend the 4-point interpolatory subdivision scheme, as a method of interpolation, to data consisting of symmetric positive definite matrices. This extension is based on an explicit formula for calculating a binary “geodetic average”. Our method generates a smooth curve of matrices, which retain many important properties of the interpolated matrices. Furthermore, the scheme is robust and easy to implement.
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Metadata
Title
Subdivision Schemes for Positive Definite Matrices
Authors
Uri Itai
Nir Sharon
Publication date
01-06-2013
Publisher
Springer-Verlag
Published in
Foundations of Computational Mathematics / Issue 3/2013
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-012-9131-y

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