The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
نویسندگان
چکیده
منابع مشابه
The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
We consider computing the singular value decomposition of a bidiagonal matrix B. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accuracy, the singular values and singular vectors of B will be determined to much higher accuracy t...
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Bidiagonal reduction is the preliminary stage for the fastest stable algorithms for computing the singular value decomposition. However, the best error bounds on bidiagonal reduction methods are of the form A + A = UBV T ; kAk 2 " M f(n)kAk 2 where B is bidiagonal, U and V are orthogonal, " M is machine precision, and f(n) is a modestly growing function of the dimensions of A. A Givens-based bi...
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The singular value decomposition (SVD) is a generalization of the eigen-decomposition which can be used to analyze rectangular matrices (the eigen-decomposition is definedonly for squaredmatrices). By analogy with the eigen-decomposition, which decomposes a matrix into two simple matrices, the main idea of the SVD is to decompose a rectangular matrix into three simple matrices: Two orthogonal m...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1991
ISSN: 0036-1429,1095-7170
DOI: 10.1137/0728076