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41.
Christine Böckmann 《Journal of Computational and Applied Mathematics》1996,70(2):207-224
A modification of the trust-region Gauss-Newton method for the identification of physical spectra is described and analysed. Local convergence results are presented. 相似文献
42.
43.
6种化学计量学法同时分光光度测定5组分的比较研究及食品分析 总被引:13,自引:0,他引:13
优化了在表面活性剂存在下以肉桂基荧光酮同时测定铝、铜、锰、锌、钴的显色折衷条件;比较研究了偏最小二乘、岭回归、多元线性回归、多元逐步回归、目标因子分析和卡尔曼滤波法用于这一体系同时测定此5组分的优缺点,结果表明对于此类所含各组分吸收光谱重叠严重且吸光度加和性欠佳体系,上述6法中以偏最小二乘和岭回归法为最适宜;经用于九种人工合成液和四种食品分析,均获满意结果,分析两种茶叶结果也与ICP-AES法一致 相似文献
44.
A new implementation of the Marquardt method for the nonlinear least-squares problem is presented. The algorithm is very simple but its performance with nine test functions is at least comparable with either Davidon-Fletcher-Powell's method or Moré's adaptive Marquardt method. 相似文献
45.
James H. Bramble Tzanio V. Kolev Joseph E. Pasciak. 《Mathematics of Computation》2005,74(252):1575-1598
In this paper we consider an approximation to the Maxwell's eigenvalue problem based on a very weak formulation of two div-curl systems with complementary boundary conditions. We formulate each of these div-curl systems as a general variational problem with different test and trial spaces, i.e., the solution space is and components in the test spaces are in subspaces of , the Sobolev space of order one on the computational domain . A finite-element least-squares approximation to these variational problems is used as a basis for the approximation. Using the structure of the continuous eigenvalue problem, a discrete approximation to the eigenvalues is set up involving only the approximation to either of the div-curl systems. We give some theorems that guarantee the convergence of the eigenvalues to those of the continuous problem without the occurrence of spurious values. Finally, some results of numerical experiments are given.
46.
H. L. Weinert R. H. Byrd G. S. Sidhu 《Journal of Optimization Theory and Applications》1980,30(2):255-268
Many of the optimal curve-fitting problems arising in approximation theory have the same structure as certain estimation problems involving random processes. We develop this structural correspondence for the problem of smoothing inaccurate data with splines and show that the smoothing spline is a sample function of a certain linear least-squares estimate. Estimation techniques are then used to derive a recursive algorithm for spline smoothing. 相似文献
47.
A note on least-squares mixed finite elements in relation to standard and mixed finite elements 总被引:3,自引:0,他引:3
** Email: brandts{at}science.uva.nl The least-squares mixed finite-element method for second-orderelliptic problems yields an approximation uh Vh H01() of thepotential u together with an approximation ph h H(div ; )of the vector field p = Au. Comparing uh with the standardfinite-element approximation of u in Vh, and ph with the mixedfinite-element approximation of p, it turns out that they arehigher-order perturbations of each other. In other words, theyare superclose. Refined a priori bounds and superconvergenceresults can now be proved. Also, the local mass conservationerror is of higher order than could be concluded from the standarda priori analysis. 相似文献
48.
<正>1引言设A_i∈S~n,i=1,…,m,定义线性算子A:S~n→R~m,AX=(A_1·X,…,A_m·X)~T,其相应的伴随算子为A~*:R~m→S~n,且A~*y=sum from i=1 to my_iA_i.X∈S~n,b∈R~m.Malick.J在[6]中讨论了如下标准半定最小二乘问题(SDLS): 相似文献
49.
当矩阵幂级数的展开式的系数产生微小摄动时,矩阵Padé-型逼近解往往变化很大.本文在矩阵Padé-型逼近研究的基础上,受Brezinski的启发,借助于误差公式和最小二乘法构造了一种稳定性和精确度均有所提高的矩阵Padé-型逼近的新方法,即最小二乘形式的矩阵Padé-型逼近(LSMPTA),并给出了LSMPTA完整的分子和分母行列式表达式.最后,通过数值实例说明了这一方法的有效性. 相似文献
50.
Approximations of random operator equations are considered where the stochastic inputs and the underlying deterministic equation are approximated simultaneously. The main convergence result asserts that, under reasonable and verifiable assumptions, a sequence of weak solutions of approximate random equations converges weakly to a weak solution of the original equation. It is shown that this theorem extends and unifies results already known. We apply our theory to approximations of random differential equations involving stochastic processes with discontinuous paths and to projection methods for nonlinear random Hammerstein integral equations in spaces of integrable functions. 相似文献