Relevant bibliographies by topics / Multiplicative Hilbert Matrix

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Multiplicative Hilbert Matrix'

Author: Grafiati
Published: 28 September 2022
Last updated: 28 January 2023

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Journal articles on the topic "Multiplicative Hilbert Matrix"

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Brevig, Ole Fredrik, Karl-Mikael Perfekt, Kristian Seip, Aristomenis G. Siskakis, and Dragan Vukotić. "The multiplicative Hilbert matrix." Advances in Mathematics 302 (October 2016): 410–32. http://dx.doi.org/10.1016/j.aim.2016.07.019.

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Perfekt, Karl-Mikael, and Alexander Pushnitski. "On the spectrum of the multiplicative Hilbert matrix." Arkiv för Matematik 56, no. 1 (2018): 163–83. http://dx.doi.org/10.4310/arkiv.2018.v56.n1.a10.

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Wu, Yuqing, and Isao Noda. "Extension of Quadrature Orthogonal Signal Corrected Two-Dimensional (QOSC 2D) Correlation Spectroscopy I: Principal Component Analysis Based QOSC 2D." Applied Spectroscopy 61, no. 10 (October 2007): 1040–44. http://dx.doi.org/10.1366/000370207782217761.

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The present study proposes a new quadrature orthogonal signal correlation (QOSC) filtering method based on principal component analysis (PCA). The external perturbation variable vector typically used in the QOSC operation is replaced with a matrix consisting of the spectral data principal components (PCs) and their quadrature counterparts obtained by using the discrete Hilbert–Noda transformation. Thus, QOSC operation can be carried out for a dataset without the explicit knowledge of the external variables information. The PCA-based QOSC filtering can be most effectively applied to two-dimensional (2D) correlation analysis. The performance of this filtering operation on the simulated spectra data set with the interference of strong random noise demonstrated that the PCA-based QOSC filtering not only eliminates the influence of signals that are unrelated to the final target but also preserves the out-of-phase information in the data matrix essential for asynchronous correlation analysis. The result of 2D correlation analysis has also demonstrated that essentially only one principal component is necessary for PCA-based QOSC to perform well. Although the present PCA-based QOSC filtering scheme is not as powerful as that based on the explicit knowledge of the external variable vector, it still can significantly improve the quality of 2D correlation spectra and enables OSC 2D to deal with the problems of losing the quadrature (or out-of-phase) information. In particular, it opens a way to perform QOSC for the spectral dataset without external variables information. The proposed approach should have wide applications in 2D correlation analysis of spectra driven by multiplicative effects in complicated systems in biological, pharmaceutical, and agriculture fields, and so on, where the explicit nature of the external perturbation cannot always be known.
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Amson, J. C., and N. Gopal Reddy. "A Hilbert algebra of Hilbert-Schmidt quadratic operators." Bulletin of the Australian Mathematical Society 41, no. 1 (February 1990): 123–34. http://dx.doi.org/10.1017/s0004972700017913.

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A quadratic operator Q of Hilbert-Schmidt class on a real separable Hilbert space H is shown to be uniquely representable as a sequence of self-adjoint linear operators of Hilbert-Schmidt class on H, such that Q(x) = Σk〈Lkx, x〉uk with respect to a Hilbert basis . It is shown that with the norm | ‖Q‖ | = (Σk ‖Lk‖2)½ and inner-product 〈〈〈Q, P〉〉〉 = Σk 〈〈Lk, Mk〉〉, together with a multiplication defined componentwise through the composition of the linear components, the vector space of all Hilbert-Schmidt quadratic operators Q on H becomes a linear H*-algebra containing an ideal of nuclear (trace class) quadratic operators. In the finite dimensional case, each Q is also shown to have another representation as a block-diagonal matrix of Hilbert-Schmidt class which simplifies the practical computation and manipulation of quadratic operators.
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Crane, Daniel K., and Mark S. Gockenbach. "The Singular Value Expansion for Arbitrary Bounded Linear Operators." Mathematics 8, no. 8 (August 12, 2020): 1346. http://dx.doi.org/10.3390/math8081346.

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The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as multiplication by a diagonal matrix. It is well known that the SVD extends naturally to a compact linear operator mapping one Hilbert space to another; the resulting representation is known as the singular value expansion (SVE). It is less well known that a general bounded linear operator defined on Hilbert spaces also has a singular value expansion. This SVE allows a simple analysis of a variety of questions about the operator, such as whether it defines a well-posed linear operator equation and how to regularize the equation when it is not well posed.
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Li, Yucheng, Hao Chen, and Wenhua Lan. "On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator." Journal of Function Spaces 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/8370139.

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Let g(z) be an n-degree polynomial (n≥2). Inspired by Sarason’s result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by using matrix manipulations, the reducing subspaces of the corresponding operator T2 on the Bergman space are characterized.
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Duggal, Bhagwati, and In-Hyoun Kim. "Structure of Iso-Symmetric Operators." Axioms 10, no. 4 (October 14, 2021): 256. http://dx.doi.org/10.3390/axioms10040256.

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For a Hilbert space operator T∈B(H), let LT and RT∈B(B(H)) denote, respectively, the operators of left multiplication and right multiplication by T. For positive integers m and n, let ▵T∗,Tm(I)=(LT∗RT−I)m(I) and δT∗,Tn(I)=(LT∗−RT)m(I). The operator T is said to be (m,n)-isosymmetric if ▵T∗,TmδT∗,Tn(I)=0. Power bounded (m,n)-isosymmetric operators T∈B(H) have an upper triangular matrix representation T=T1T30T2∈B(H1⊕H2) such that T1∈B(H1) is a C0.-operator which satisfies δT1∗,T1n(I|H1)=0 and T2∈B(H2) is a C1.-operator which satisfies AT2=(Vu⊕Vb)|H2A, A=limt→∞T2∗tT2t, Vu is a unitary and Vb is a bilateral shift. If, in particular, T is cohyponormal, then T is the direct sum of a unitary with a C00-contraction.
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Duggal, Bhagwati, and In-Hyoun Kim. "Structure of Iso-Symmetric Operators." Axioms 10, no. 4 (October 14, 2021): 256. http://dx.doi.org/10.3390/axioms10040256.

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For a Hilbert space operator T∈B(H), let LT and RT∈B(B(H)) denote, respectively, the operators of left multiplication and right multiplication by T. For positive integers m and n, let ▵T∗,Tm(I)=(LT∗RT−I)m(I) and δT∗,Tn(I)=(LT∗−RT)m(I). The operator T is said to be (m,n)-isosymmetric if ▵T∗,TmδT∗,Tn(I)=0. Power bounded (m,n)-isosymmetric operators T∈B(H) have an upper triangular matrix representation T=T1T30T2∈B(H1⊕H2) such that T1∈B(H1) is a C0.-operator which satisfies δT1∗,T1n(I|H1)=0 and T2∈B(H2) is a C1.-operator which satisfies AT2=(Vu⊕Vb)|H2A, A=limt→∞T2∗tT2t, Vu is a unitary and Vb is a bilateral shift. If, in particular, T is cohyponormal, then T is the direct sum of a unitary with a C00-contraction.
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Peng, Wujian, and Qun Lin. "A Non-Krylov Subspace Method for Solving Large and Sparse Linear System of Equations." Numerical Mathematics: Theory, Methods and Applications 9, no. 2 (May 2016): 289–314. http://dx.doi.org/10.4208/nmtma.2016.y14014.

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AbstractMost current prevalent iterative methods can be classified into the socalled extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional Krylov subspace methods which always depend on the matrix-vector multiplication with a fixed matrix, the newly introduced methods (the so-called (progressively) accumulated projection methods, or AP (PAP) for short) use a projection matrix which varies in every iteration to form a subspace from which an approximate solution is sought. More importantly an accelerative approach (called APAP) is introduced to improve the convergence of PAP method. Numerical experiments demonstrate some surprisingly improved convergence behavior. Comparison between benchmark extended Krylov subspace methods (Block Jacobi and GMRES) are made and one can also see remarkable advantage of APAP in some examples. APAP is also used to solve systems with extremely ill-conditioned coefficient matrix (the Hilbert matrix) and numerical experiments shows that it can bring very satisfactory results even when the size of system is up to a few thousands.
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LONG, YINXIANG, DAOWEN QIU, and DONGYANG LONG. "AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES." International Journal of Quantum Information 09, no. 04 (June 2011): 1101–12. http://dx.doi.org/10.1142/s0219749911007514.

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In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.
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Dissertations / Theses on the topic "Multiplicative Hilbert Matrix"

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Benyamine, Charif Abdallah. "Sections finies d'inégalités multiplicatives de Hilbert et multiplicateurs de l'espace de Dirichlet." Thesis, Bordeaux, 2022. http://www.theses.fr/2022BORD0187.

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Nous étudions deux problèmes. Le premier concerne les sections finies de l'inégalité multiplicative de Hilbert. Nous donnons le comportement asymptotique de la meilleure constante $lambda_n$ dans l'inégalité$$Big|sum_{i,j=2}^{n}frac{a_ioverline{a_j}}{ijlog(ij)}Big|leq lambda_n sum_{i=2}^n|a_i|^2.$$Nous donnons aussi le comportement asymptotique de la version $ell^p$ des sections finies de l'inégalité multiplicative de Hilbert.Le deuxième problème concerne l'appartenance des fonctions distance à l'algèbre des multiplicateurs de l'espace de Dirichlet. Les fonctions distance sont les fonctions extérieures dont les valeurs au bord ne dépendent que de la distance par rapport à un ensemble fermé du cercle unité de mesure nulle. Nous donnons une estimation de l'intégrale de Dirichlet d'une fonction distance pour qu'elle appartienne à l'algèbre des multiplicateurs
We study two problems. The first one concerns finite sections of the Hilbert multiplicative inequality. We give the asymptotic behaviour of the best constant $lambda_n$ in the inequality$$Big|sum_{i,j=2}^{n}frac{a_ioverline{a_j}}{ijlog(ij)}Big|leq lambda_n sum_{i=2}^n|a_i|^2.$$We also give the asymptotic behaviour of the $ell^p$ version of the finite sections of the Hilbert multiplicative inequality.The second problem concerns the membership of the multiplier algebra of the Dirichlet space of so-called distance functions, namely outer functions whose boundary values depend only on distance to a closed subset of measure zero. We establish an estimate for the Dirichlet integral of such function to belong to the multiplier algebras of the Dirichlet space
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Book chapters on the topic "Multiplicative Hilbert Matrix"

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Yzelman, Albert-Jan N., and Rob H. Bisseling. "A Cache-Oblivious Sparse Matrix–Vector Multiplication Scheme Based on the Hilbert Curve." In Mathematics in Industry, 627–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25100-9_73.

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