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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We consider the problem of updating the SVD when augmenting a “tall thin” matrix, i.e., a rectangular matrix AâRmÃn with mâ«n. Supposing that an SVD of A is already known, and given a matrix BâRmÃnâ², we derive an efficient method to compute and efficiently store the SVD of the augmented matrix [AB]âRmÃ(n+nâ²). 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
Journal: Linear Algebra and its Applications - Volume 561, 15 January 2019, Pages 41-62
نویسندگان
Juan Manuel Peña, Tomas Sauer,