The Experts below are selected from a list of 810 Experts worldwide ranked by ideXlab platform
Masaaki Miyakoshi - One of the best experts on this subject based on the ideXlab platform.
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Kernel-induced sampling theorem
2016Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:Abstract—A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is dis-cussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to per-fectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space cor-responding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points. Index Terms—Gramian matrix, Hilbert space, Orthogonal pro-jection, reproducing kernel, sampling theorem. I
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Kernel-Induced Sampling Theorem
2010Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points.
Akira Tanaka - One of the best experts on this subject based on the ideXlab platform.
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Kernel-induced sampling theorem
2016Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:Abstract—A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is dis-cussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to per-fectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space cor-responding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points. Index Terms—Gramian matrix, Hilbert space, Orthogonal pro-jection, reproducing kernel, sampling theorem. I
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Kernel-Induced Sampling Theorem
2010Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points.
Daniel Neuhauser - One of the best experts on this subject based on the ideXlab platform.
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real space Orthogonal Projector augmented wave method
2020Co-Authors: Daniel NeuhauserAbstract:The Projector-augmented-wave (PAW) method of Bl\"ochl makes smooth but nonOrthogonal orbitals. Here we show how to make a PAW Orthogonal using a cheap transformation of the wave functions. We show that the resulting Orthogonal PAW (OPAW), applied for density functional theory, reproduces (for a large variety of solids) band gaps from the abinit package. OPAW combines the underlying Orthogonality of norm-conserving pseudopotentials with the large grid spacings and small energy cutoffs in PAW. The OPAW framework can also be combined with other electronic structure theory methods.
Ivan V Oseledets - One of the best experts on this subject based on the ideXlab platform.
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a Projector splitting integrator for dynamical low rank approximation
2013Co-Authors: Christian Lubich, Ivan V OseledetsAbstract:The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors of the matrices, which need to be solved numerically. We propose and analyze a fully ex- plicit, computationally inexpensive integrator that is based on splitting the Orthogonal Projector onto the tangent space of the low-rank manifold. As is shown by theory and illustrated by numerical experiments, the integrator enjoys robustness properties that are not shared by any standard numerical integrator. This robustness can be exploited to change the rank adaptively. Another application is in optimization algorithms for low-rank matrices where truncation back to the given low rank can be done efficiently by applying a step of the integrator proposed here.
Hideyuki Imai - One of the best experts on this subject based on the ideXlab platform.
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Kernel-induced sampling theorem
2016Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:Abstract—A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is dis-cussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to per-fectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space cor-responding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points. Index Terms—Gramian matrix, Hilbert space, Orthogonal pro-jection, reproducing kernel, sampling theorem. I
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Kernel-Induced Sampling Theorem
2010Co-Authors: Akira Tanaka, Hideyuki Imai, Masaaki MiyakoshiAbstract:A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the Orthogonal Projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points.
