کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10997861 1337268 2019 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
SVD update methods for large matrices and applications
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
SVD update methods for large matrices and applications
چکیده انگلیسی
We consider the problem of updating the SVD when augmenting a “tall thin” matrix, i.e., a rectangular matrix A∈Rm×n with m≫n. Supposing that an SVD of A is already known, and given a matrix B∈Rm×n′, we derive an efficient method to compute and efficiently store the SVD of the augmented matrix [AB]∈Rm×(n+n′). This is an important tool for two types of applications: in the context of principal component analysis, the dominant left singular vectors provided by this decomposition form an orthonormal basis for the best linear subspace of a given dimension, while from the right singular vectors one can extract an orthonormal basis of the kernel of the matrix. We also describe two concrete applications of these concepts which motivated the development of our method and to which it is very well adapted.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 561, 15 January 2019, Pages 41-62
نویسندگان
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