The Development and Comparison of Robust Methodsfor Estimating the Fundamental Matrix
International Journal of Computer Vision
Incremental Tensor Subspace Learning and Its Applications to Foreground Segmentation and Tracking
International Journal of Computer Vision
Dynamic normal forms and dynamic characteristic polynomial
Theoretical Computer Science
An efficient algorithm for rank and subspace tracking
Mathematical and Computer Modelling: An International Journal
Computational Statistics & Data Analysis
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Let $A$ be a matrix with known singular values and left and/or right singular vectors, and let $A'$ be the matrix obtained by deleting a row from $A$. We present efficient and stable algorithms for computing the singular values and left and/or right singular vectors of $A'$. We also show that the problem of computing the singular values of $A'$ is well conditioned when the left singular vectors of $A$ are given, but can be ill conditioned when they are not. Our algorithms reduce the problem to computing the eigendecomposition or singular value decomposition of a matrix that has a simple structure, and solve the reduced problem via finding the roots of a secular equation. Previous algorithms of this type can be unstable and always solve the ill-conditioned problem.