A gradient-type algorithm optimizing the coupling between matrices
نویسندگان
چکیده
منابع مشابه
A gradient-type algorithm optimizing the coupling between matrices
In this paper, we consider the problem of maximizing the coupling between the isometric projections of two square matrices of dimensions m and n. This coupling is defined as an inner product between the matrices. This is a non-convex optimization problem with isometry constraints on the variables. The optimization set is an equinormed set and we develop a gradient-type algorithm to solve the pr...
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چکیده ندارد.
Optimizing the Coupling Between Two Isometric Projections of Matrices
In this paper, we analyze the coupling between the isometric projections of two square matrices. These two matrices of dimensions m×m and n×n are restricted to a lower k-dimensional subspace under isometry constraints. We maximize the coupling between these isometric projections expressed as the trace of the product of the projected matrices. First we connect this problem to notions such as the...
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The well known conjugate gradient algorithm (cg-algorithm), introduced by Hestenes & Stiefel, [1952] intended for real, symmetric, positive definite matrices works as well for complex matrices and has the same typical convergence behavior. It will also work, not generally, but in many cases for hermitean, but not necessarily positive definite matrices. We shall show, that the same behavior is s...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.10.015