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排序方式: 共有959条查询结果,搜索用时 15 毫秒
951.
We study operators of the form Lu = — G(t) u(t) in L2([t0δ, t0 + δ], H) with = L2 ([t0δ, t0 + δ], H ) in the neighbourhood [t0δ, 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   
953.
陈玺  屈龙江  李超 《数学杂志》2017,37(1):138-144
本文研究了有限域上只有零解的n元n次方程的结构问题.利用对有限域上不可约多元多项式在其扩域中的分解特征的刻画,结合Chevalley定理,得到了有限域上n元n次方程只有零解的一个充要条件,并给出这类方程的一些新的具体构造.  相似文献   
954.
955.
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.
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 A = U T V $$ \mathbf{\mathsf{A}}=\mathbf{\mathsf{UT}}{\mathbf{\mathsf{V}}}^{\ast } $$ , where U $$ \mathbf{\mathsf{U}} $$ and V $$ \mathbf{\mathsf{V}} $$ are orthogonal and T $$ \mathbf{\mathsf{T}} $$ is trapezoidal (or triangular if A $$ \mathbf{\mathsf{A}} $$ 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.
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.
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