2016/11/23 by Kaoru Yamamoto, Yamamoto, Kaoru, Yongxin Chen +7
Mathematics · #81R60 #93A99 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Optimization and Control (math.OC) #Point processes and geometric inequalities #math.OC #msc:81R60 #msc:93A99
paper · pdf · doi:10.48550/arxiv.1611.07945
4 pages, 6 figures
arxiv created 2016/11/23 · openalex publication_date 2016/11/23 · arxiv updated 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider certain matricial analogues of optimal mass transport of positive definite matrices of equal trace. The framework is motivated by the need to devise a suitable geometry for interpolating positive definite matrices in ways that allow controlling the apparent tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Indeed, motivation for this work is provided by power spectral analysis of multivariate time series where, linear interpolation between matrix-valued power spectra generates push-pop artifacts. Push-pop of power distribuion is objectionable as it corresponds to unrealistic response of scatterers.