A Riemannian Limited-Memory BFGS Algorithm for Computing the Matrix Geometric Mean
نویسندگان
چکیده
منابع مشابه
Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method
A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...
متن کاملRiemannian BFGS Algorithm with Applications
In this paper, we present a retraction-based Riemannian BFGS approach (RBFGS). Of particular interest is the choice of transport used to move information between tangent spaces and the different ways of implementing the RBFGS algorithm. We consider parallel translation along a geodesic and vector transport by projection on the unit sphere and the compact Stiefel manifold.
متن کاملA Numerical Study of Limited Memory BFGS
The application of quasi-Newton methods is widespread in numerical optimization. Independently of the application, the techniques used to update the BFGS matrices seem to play an important role in the performance of the overall method. In this paper we address precisely this issue. We compare two implementations of the limited memory BFGS method for large-scale unconstrained problems. They diie...
متن کاملCriterion for the Limited Memory BFGS Algorithm for Large Scale Nonlinear Optimization
This paper studies recent modi cations of the limited memory BFGS (L-BFGS) method for solving large scale unconstrained optimization problems. Each modi cation technique attempts to improve the quality of the L-BFGS Hessian by employing (extra) updates in certain sense. Because at some iterations these updates might be redundant or worsen the quality of this Hessian, this paper proposes an upda...
متن کاملA regularized limited-memory BFGS method for unconstrained minimization problems
The limited-memory BFGS (L-BFGS) algorithm is a popular method of solving large-scale unconstrained minimization problems. Since LBFGS conducts a line search with the Wolfe condition, it may require many function evaluations for ill-posed problems. To overcome this difficulty, we propose a method that combines L-BFGS with the regularized Newton method. The computational cost for a single iterat...
متن کاملذخیره 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: Procedia Computer Science
سال: 2016
ISSN: 1877-0509
DOI: 10.1016/j.procs.2016.05.534