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。这叫 Leve
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...
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...
Sherman-Morrison-Woodburyformula Consideranon-singularnxnmatrixA B=A+uv T whereuandvarenx1vectors.The’outer’productofuandvisannxn matrixofrankone.IfwehavecomputedtheinverseofA,isthereashort-cut forthecomputationofB? TheSherman-Morrison-Woodburyformulashowshowtoupdatetheinverseof amatrixalteredbytheadditi...
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 ...
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 ...
Linear system Direct methods Sherman–Morrison formula Approximate inverse preconditioner View PDFReferences [1] J. Sherman, W.J. Morrison Adjustment of an inverse matrix corresponding to a change in one element of a given matrix Ann. Math. Statistics, 21 (1950), pp. 124-127 CrossrefGoogle Sch...
A new method is introduced based on the Sherman–Morrison matrix inversion formula for calculation of the optimal absorber parameter values for attachment to a damped multi-degree of freedom system. The new method can be used to minimize the motion of particular physical masses or modes of ...
Generalized Sherman–Morrison–Woodbury formula based algorithm for the inverses of opposite-bordered tridiagonal matrices Matrix inverse computation is one of the fundamental mathematical problems of linear algebra and has been widely used in many fields of science and enginee... JT Jia,T Sogabe - ...
GPS Solutions (2023) 27:44 https://doi.org/10.1007/s10291-022-01384-3 ORIGINAL ARTICLE Fast satellite selection algorithm for GNSS multi‑system based on Sherman–Morrison formula Junpeng Shi1 · Kezhao Li1 · Lin Chai2 · Lingfeng Liang1 · Chendong Tian1 ·...