Sherman–Morrison formula的内容是: 只要满足分母不为零的条件,就可以incremental的求矩阵的逆了。 这在机器学习中有什么用处呢?这对那些本身是 很多向量外积和 的矩阵尤为有用。 比如回归损失如果是E: 那么黑森矩阵就可以写为: 在训练快完成时,第二项很小,我们就可以用第一项(向量外积和)来逼近这个黑森矩阵了。
舍尔曼-莫里森公式(Sherman-Morrison formula)是线性代数中的一个重要公式,用于计算矩阵的逆在受到秩-1更新后的新逆矩阵。 具体来说,给定一个可逆矩阵 A 和一个向量 u 和 v ,舍尔曼-莫里森公式可以用来计算 (A + uv^T)^{-1} ,其中 uv^T 是一个秩-1矩阵。 公式形式 舍尔曼-莫里森公式可以表示为: (A...
The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v (1) for two vectors u and v, then the Sherman-Morrison formula is (A+u tens
Sherman-Morrison-Woodbury Formula阐述了以下内容：当可逆[公式] 阶方阵 [公式] 受到较小的秩 [公式] 扰动，即[公式] 时，扰动后的矩阵依然保持可逆性，并且[公式]。需要注意的是，前提条件是[公式] 必须是可逆的。Golub的【Matrix Computation】直接给出了这个定理，但并未说明其推导过程。下面将给...
1) Sherman-Morrison-Woodbury formula SMW公式 2) SMW pile SMW桩 1. For the sake of safety and economy,the distance between SMW piles is optimized and reasonable design proposal is obtained. 提出了门架式围护结构计算模型,模型中将桩受到的地基土抗力简化为弹性支撑;并对双排SMW桩门架式围护的桩间...
1 Sherman-Morrison-Woodburyformula Consideranon-singularnxnmatrixA B=A+uv T whereuandvarenx1vectors.The’outer’productofuandvisannxn matrixofrankone.IfwehavecomputedtheinverseofA,isthereashort-cut forthecomputationofB? TheSherman-Morrison-Woodburyformulashowshowtoupdatetheinverseof amatrixalteredbythead...
Sherman-Morrison-Woodbury formula for the core inverse of matrices and its applications YANG Hong",ZHONG Jin1,MA Bolin2 (1.Faculty of Science,Jiangxi University of Science and Technology,Ganzhou341000,Jiangxi,China;2.School of Mathematics and Information Engineering,Jiaxing University,Jiaxing314001,...
Sherman-Morrison-Woodbury 下载积分: 1000 内容提示: Bindel, Fall 2009Matrix Computations (CS 6210)Week 5: Wednesday, Sep 23Sherman-Morrison-WoodburyThe Sherman-Morrison formula describes the solution of A+uvTwhen thereis already a factorization for A. An easy way to derive the formula is ...
Sherman–Morrison Formula We will begin with the simpler case of a rank- perturbation: , where and are -vectors, and we consider first the case where . We might expect that for some (consider a binomial expansion of the inverse). Multiplying out, we obtain ...