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Matrix data sets are common nowadays like in biomedical imaging where theDiffusion Tensor Magnetic Resonance Imaging (DT-MRI) modality produces datasets of  3D symmetric positive definite matrices anchored at voxel positions capturingthe anisotropic diffusion properties of water molecules in biological tissues.The space of symmetric matrices can be partially ordered using the L\"ownerordering, and computing extremal matrices dominating a given set of matrices isa basic primitive used in matrix-valued signal processing. In this letter, wedesign a fast and easy-to-implement iterative algorithm to approximatearbitrarily finely these extremal matrices. Finally, we discuss on extensionsto matrix clustering.

Fast $(1+\epsilon)$-approximation of the L\"owner extremal matrices of high-dimensional symmetric matrices