Geometries on the cone of positive-definite matrices derived from the power potential and their relation to the power means
Sign Up to like & getrecommendations! Published in 2021 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2021.12.012
Abstract: We study a Riemannian metric on the cone of symmetric positive-definite matrices obtained from the Hessian of the power potential function (1 − det(X))/β. We give explicit expressions for the geodesics and distance function, under… read more here.
Keywords: definite matrices; power potential; positive definite; power ... See more keywords
Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices
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DOI: 10.1080/01621459.2019.1700129
Abstract: Abstract Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary time series.… read more here.
Keywords: positive definite; intrinsic wavelet; hermitian positive; wavelet ... See more keywords
A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Computational Physics"
DOI: 10.4208/cicp.oa-2018-0053
Abstract: We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their… read more here.
Keywords: root; general algorithm; positive definite; symmetric positive ... See more keywords