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1.
Ieva
Dauickait Amos S. Lawless Jennifer A. Scott Peter Jan van Leeuwen 《Numerical Linear Algebra with Applications》2020,27(5)
We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds. 相似文献
2.
3.
In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class
of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve
model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given
for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively.
Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature
for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions
for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there
exist UMRE estimators of parameters in the variance components model are obtained for the first time. 相似文献
4.
The dependence of the beam propagation factor (M
2 parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively
studied. Our investigations show that the M
2 parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due
to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration
associated with the thermal lens induced by the pump beam. Such dependency of M
2 parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd3+ -doped GdVO4 crystal and the values of α and β parameters were estimated from the experimentally measured data points. 相似文献
5.
本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果 相似文献
6.
7.
Xuguang Lu 《Journal of statistical physics》2006,124(2-4):517-547
The paper considers macroscopic behavior of a Fermi–Dirac particle system. We prove the L
1-compactness of velocity averages of weak solutions of the Boltzmann equation for Fermi–Dirac particles in a periodic box with the collision kernel b(cos θ)|ρ−ρ
*|γ, which corresponds to very soft potentials: −5 < γ ≤ −3 with a weak angular cutoff: ∫0
π
b(cos θ)sin 3θ dθ < ∞. Our proof for the averaging compactness is based on the entropy inequality, Hausdorff–Young inequality, the L
∞-bounds of the solutions, and a specific property of the value-range of the exponent γ. Once such an averaging compactness is proven, the proof of the existence of weak solutions will be relatively easy. 相似文献
8.
9.
关于AOR迭代法的研究 总被引:5,自引:0,他引:5
陈恒新 《应用数学与计算数学学报》2002,16(1):40-46
本文论证了严格对角占优矩阵之AOR法的误差估计式中的误差估计常数hγ,ω(0≤γ≤ω0)的最小值是h1,1. 相似文献
10.