Computing the Karcher mean of symmetric positive definite matrices

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Riemannian quasi-Newton method for computing the Karcher mean of symmetric positive definite matrices

This paper tackles the problem of computing the Karcher mean of a collection of symmetric positive-definite matrices. We present a concrete limited-memory Riemannian BFGS method to handle this computational task. We also provide methods to produce efficient numerical representations of geometric objects on the manifold of symmetric positive-definite matrices that are required for Riemannian opt...

متن کامل

A proximal technique for computing the Karcher mean of symmetric positive definite matrices

This paper presents a proximal point approach for computing the Riemannian or intrinsic Karcher mean of, n×n, symmetric positive definite (SPD) matrices. Our method derives from proximal point algorithm with Schur decomposition developed to compute minimum points of convex functions on SPD matrices set when it is seen as a Hadamard manifold. The main idea of the original method is preserved. Ho...

متن کامل

A Majorization-Minimization Algorithm for the Karcher Mean of Positive Definite Matrices

An algorithm for computing the Karcher mean of n positive definite matrices is proposed, based on the majorization-minimization (MM) principle. The proposed MM algorithm is parameter-free, does not need to choose step sizes, and has a theoretical guarantee of asymptotic linear convergence.

متن کامل

Karcher Means and Karcher Equations of Positive Definite Operators

The Karcher or least-squares mean has recently become an important tool for the averaging and studying of positive definite matrices. In this paper we show that this mean extends, in its general weighted form, to the infinite-dimensional setting of positive operators on a Hilbert space and retains most of its attractive properties. The primary extension is via its characterization as the unique...

متن کامل

DDtBe for Band Symmetric Positive Definite Matrices

We present a new parallel factorization for band symmetric positive definite (s.p.d) matrices and show some of its applications. Let A be a band s.p.d matrix of order n and half bandwidth m. We show how to factor A as A =DDt Be using approximately 4nm2 jp parallel operations where p =21: is the number of processors. Having this factorization, we improve the time to solve Ax = b by a factor of m...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2013

ISSN: 0024-3795

DOI: 10.1016/j.laa.2011.08.052