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排序方式: 共有959条查询结果,搜索用时 15 毫秒
951.
Mahir Hasanov 《Mathematische Nachrichten》2001,228(1):145-154
We study operators of the form Lu = — G(t) u(t) in L2([t0 — δ, t0 + δ], H) with = L2 ([t0— δ, t0 + δ], H ) in the neighbourhood [t0— δ, t0 + δ] of a point t0 ∈ ℝ1. Such problems arise in questions on local solvability of partial differential equations (see [6] and [7]). For these operators,one of the major questions is if they are invertible in a neighbourhood of a point t ∈ ℝ1. To solve this problem we establish needed commutator estimates. Using the commutator estimates and factorization theorems for nonanalytic operator-functions we give additional conditions for the nonanalytic operator -function G(t) and show that the operator L (or ) with some boundary conditions is local invertible. 相似文献
952.
Letm 3 be an odd integer and let k, n, and s 3 be positive integers. We present sufficient conditions for the existence of C-factorizations of (Cmk)n. We show these conditions to be necessary when m is prime. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 173–183, 1999 相似文献
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955.
Jean‐Philip Royer Nadge Thirion‐Moreau Pierre Comon Roland Redon Stphane Mounier 《Journal of Chemometrics》2015,29(4):253-265
We consider blind source separation in chemical analysis focussing on the 3D fluorescence spectroscopy framework. We present an alternative method to process the Fluorescence Excitation‐Emission Matrices (FEEM): first, a preprocessing is applied to eliminate the Raman and Rayleigh scattering peaks that clutter the FEEM. To improve its robustness versus possible improper settings, we suggest to associate the classical Zepp's method with a morphological image filtering technique. Then, in the second stage, the Canonical Polyadic (CP or Candecomp/Parafac) decomposition of a nonnegative three‐way array has to be computed. In the fluorescence spectroscopy context, the constituent vectors of the loading matrices should be nonnegative (since standing for spectra and concentrations). Thus, we suggest a new nonnegative third order CP decomposition algorithm (NNCP) based on a nonlinear conjugate gradient optimization algorithm with regularization terms and periodic restarts. Computer simulations performed on real experimental data are provided to enlighten the effectiveness and robustness of the whole processing chain and to validate the approach. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
956.
A geometric intrinsic pre-processing algorithm(GPA for short) for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023). Different from traditional preconditioning, the authors apply the intrinsic geometric invariance, the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG = GB and AG = GA, where G satisfies Gm= I, m << dim(G). A large scale system solvers can be replaced t... 相似文献
957.
Nathan Heavner Chao Chen Abinand Gopal Per-Gunnar Martinsson 《Numerical Linear Algebra with Applications》2023,30(6):e2515
Standard rank-revealing factorizations such as the singular value decomposition (SVD) and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms to cast most operations in terms of the Level-3 BLAS. This article presents two alternative algorithms for computing a rank-revealing factorization of the form , where and are orthogonal and is trapezoidal (or triangular if is square). Both algorithms use randomized projection techniques to cast most of the flops in terms of matrix-matrix multiplication, which is exceptionally efficient on the GPU. Numerical experiments illustrate that these algorithms achieve significant acceleration over finely tuned GPU implementations of the SVD while providing low rank approximation errors close to that of the SVD. 相似文献
958.
An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions 下载免费PDF全文
The paper investigates the robustness and parallel scaling properties of
a novel physical factorization preconditioner with algebraic multigrid subsolves in
the iterative solution of a cell-centered finite volume discretization of the three-dimensional multi-group radiation diffusion equations. The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and
approximate the left-hand block matrix selectively spurred by parallel processing
considerations. The spectral property of the preconditioned matrix is then analyzed.
The practical strategy is considered sequentially and in parallel. Finally, numerical results illustrate the numerical robustness, computational efficiency and parallel
strong and weak scalabilities over the real-world structured and unstructured coupled problems, showing its competitiveness with many existing block preconditioners. 相似文献
959.