Least Square Problems, Qr Decomposition, and Svd Decomposition
نویسنده
چکیده
We review basics on least square problems. The material is mainly taken from books [2, 1, 3]. We consider an overdetermined system Ax = b where Am×n is a tall matrix, i.e., m > n. We have more equations than unknowns and in general cannot solve it exactly.
منابع مشابه
E cient Computation of the Singular Value Decomposition with Applications to Least Squares Problems
We present a new algorithm for computing the singular value decomposition (SVD) of a matrix. The algorithm is based on using divide-and-conquer to compute the SVD of a bidiagonal matrix. Compared to the previous algorithm (based on QR-iteration) the new algorithm is at least 9 times faster on bidiagonal matrices of dimension n = 400, when running on a DEC Alpha with optimized BLAS. The speedup ...
متن کاملKernel-based Weighted Discriminant Analysis with QR Decomposition and Its Application to Face Recognition
Kernel discriminant analysis (KDA) is a widely used approach in feature extraction problems. However, for high-dimensional multi-class tasks, such as faces recognition, traditional KDA algorithms have a limitation that the Fisher criterion is non-optimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents two variants of KDA called ...
متن کاملSome Asymptotic Behaviors Associated with Matrix Decompositions
We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition.
متن کاملOptimum Signal Processing 2002 – 2007 SVD , PCA , KLT , CCA , and All That
1 Vector and Matrix Norms, 2 2 Subspaces, Bases, and Projections, 3 3 The Fundamental Theorem of Linear Algebra, 7 4 Solving Linear Equations, 7 5 The Singular Value Decomposition, 13 6 Moore-Penrose Pseudoinverse, 18 7 Least-Squares Problems and the SVD, 20 8 Condition Number, 22 9 Reduced-Rank Approximation, 23 10 Regularization of Ill-Conditioned Problems, 29 11 SVD and Signal Processing, 30...
متن کاملAn algorithm for solving rank-deficient scaled total least square problems
The scaled total least square (STLS) problem, introduced by B.D. Rao in 1997, unifies both the total least square (TLS) and the least square (LS) problems. The STLS problems can be solved by the singular value decomposition (SVD). In this paper, we give a rank-revealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis is presented. Our numerical experime...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015