Subdivision Schemes for Positive Definite Matrices

Uri Itai, Nir Sharon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)347-369
Number of pages23
JournalFoundations of Computational Mathematics
Issue number3
StatePublished - Jun 2013


  • Interpolation
  • Nonlinear subdivision scheme
  • Positive definite matrix


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