For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U ...For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.展开更多
A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be...A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be computed in parallel using the sametransformation.We also prove that some kind of Toeplltz-block matrices can he transformed into the corresponding block-Toeplitz matrices.展开更多
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, no...Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.展开更多
基金Supported by the President Foundation of Chinese Academy of Science and Specialized Research Fund for the Doctorial Progress of Higher Education under Grant No.20070358009
文摘For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.
文摘A fast algorithm FBTQ is presented which computes the QR factorization a block-Toeplitz matrix A (A∈R) in O(mns3) multiplications. We prove that the QR decomposition of A and the inverse Cholesky decomposition can be computed in parallel using the sametransformation.We also prove that some kind of Toeplltz-block matrices can he transformed into the corresponding block-Toeplitz matrices.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) (Grant No. RGP 228051)
文摘Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.
