Perbandingan Algoritma Golub Kahan danQR Simetri untuk Dekomposisi Nilai Singular
نویسندگان
چکیده
منابع مشابه
Generalized Golub-Kahan Bidiagonalization and Stopping Criteria
The Golub–Kahan bidiagonalization algorithm has been widely used in solving leastsquares problems and in the computation of the SVD of rectangular matrices. Here we propose an algorithm based on the Golub–Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes a...
متن کاملReorthogonalization for Golub–kahan–lanczos Bidiagonal Reduction: Part Ii – Singular Vectors
where U ∈ R is left orthogonal, V ∈ R is orthogonal, and B ∈ R is bidiagonal. When the Lanczos recurrence is implemented in finite precision arithmetic, the columns of U and V tend to lose orthogonality, making a reorthogonalization strategy necessary to preserve convergence of the singular values. A new strategy is proposed for recovering the left singular vectors. When using that strategy, it...
متن کاملGCV for Tikhonov regularization via global Golub-Kahan decomposition
Generalized Cross Validation (GCV) is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small-scale problems, but prohibitively expensive to compute for large-scale ones. This paper describes a novel method, based on Gauss-type quadrature, for determining up...
متن کاملReorthogonalization for the Golub-Kahan-Lanczos bidiagonal reduction
The Golub–Kahan–Lanczos (GKL) bidiagonal reduction generates, by recurrence, the matrix factorization of X ∈ Rm×n,m ≥ n, given by X = U BV T where U ∈ Rm×n is left orthogonal, V ∈ Rn×n is orthogonal, and B ∈ Rn×n is bidiagonal. When the GKL recurrence is implemented in finite precision arithmetic, the columns of U and V tend to lose orthogonality, making a reorthogonalization strategy necessary...
متن کاملA Golub-Kahan-Type Reduction Method for Matrix Pairs
We describe a novel method for reducing a pair of large matrices {A,B} to a pair of small matrices {H,K}. The method is an extension of Golub–Kahan bidiagonalization to matrix pairs, and simplifies to the latter method when B is the identity matrix. Applications to Tikhonov regularization of large linear discrete ill-posed problems are described. In these problems the matrix A represents a disc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Limits: Journal of Mathematics and Its Applications
سال: 2006
ISSN: 2579-8936,1829-605X
DOI: 10.12962/j1829605x.v3i1.1393