We provide an expression for the derivative of the weighted matrix geometric mean, with respect to both the matrix arguments and the weights, that can be easily translated to an algorithm for its computation. As an application, we consider the problem of the approximate decomposition of a tensor...
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aWhere M is the mass matrix, δ (t)′′ is the 2nd time derivative of the displacementδ (t) (i.e., the acceleration), δ (t)′ is the velocity, C is a damping matrix, K is the stiffness matrix, and P(t) is the force vector. 那里M是许多矩阵, δ (t) ′ ′是displacement...
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我在网上找到了关于核范数求导的两种方式,一种是论文里常用的Singular Value Thresholding(SVT)方法,另外一种是网上流传的通过SVD的方式直接求导的方式。 1. Singular Value Thresholding 这种方法最早是针对矩阵补全的问题提出的,在论文《A Singular Value Thresholding Algorithm for Matrix Com... ...
There are several definitions for the matrix derivative, which are all given through different calculating rules. This paper demonstrates that all these definitions may be considered as special cases of the general definition of the derivative in normed spaces. They only present the derivative in ...
It is well-known that the logarithmic derivative μ[ A] of a square matrix A has its value no less than the maximum real part p of the eigenvalues of A and there exist matrices A such that μ[ A] > p with respect to any norm in C n. The purpose of this note is to show that...
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