主分量分析在大气科学研究中的应用日益广泛,但对其应用的可行性和可靠性的研究则比较欠缺.本文对主分量分析的三种方法,即非旋转主分量、正交旋转的方差极大法和斜交旋转的Harris-Kaiser Case ⅡB^TB法,在区域气候分型研究中的应用进...主分量分析在大气科学研究中的应用日益广泛,但对其应用的可行性和可靠性的研究则比较欠缺.本文对主分量分析的三种方法,即非旋转主分量、正交旋转的方差极大法和斜交旋转的Harris-Kaiser Case ⅡB^TB法,在区域气候分型研究中的应用进行了计算分析和精度拟合,同时进行了区域分割和Monte-Carlo模拟的统计试验.结果表明,非旋转主分量的分型拟合精度不佳,两种旋转主分量方法的效果很好,其中正交旋转又优于斜交旋转.区域范围的变化对旋转主分量方法的分型结果影响不大,对非旋转主分量分析的影响较大.样本大小的变化对主分量分析的各种方法无明显影响.展开更多
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute t...We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.展开更多
Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes i...Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.展开更多
Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the...Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the discretization errors in SEM could be reduced exponentially to machine zero so that the spectral convergence rate can be achieved. Inherited the advantage of FEM, SEM can enhance resolution via both h-type and p-type mesh-refinement. A penalty method was utilized to compute force fields in particulate flows involving freely moving rigid particles. Results were analyzed and comparisons were made;therefore, this penalty-implemented SEM was proven to be a viable method for two-phase flow problems.展开更多
文摘主分量分析在大气科学研究中的应用日益广泛,但对其应用的可行性和可靠性的研究则比较欠缺.本文对主分量分析的三种方法,即非旋转主分量、正交旋转的方差极大法和斜交旋转的Harris-Kaiser Case ⅡB^TB法,在区域气候分型研究中的应用进行了计算分析和精度拟合,同时进行了区域分割和Monte-Carlo模拟的统计试验.结果表明,非旋转主分量的分型拟合精度不佳,两种旋转主分量方法的效果很好,其中正交旋转又优于斜交旋转.区域范围的变化对旋转主分量方法的分型结果影响不大,对非旋转主分量分析的影响较大.样本大小的变化对主分量分析的各种方法无明显影响.
文摘We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
基金supported by the Program for New Century Excellent Talents in Universityof China (Grant No. NCET-07-0454)National Natural Science Foundation of China (Grant No. 10971107)the Fundamental Research Funds for the Central Universities (Grant No. 10QNJJ003)
文摘Latin hypercube design and uniform design are two kinds of most popular space-filling designs for computer experiments. The fact that the run size equals the number of factor levels in a Latin hypercube design makes it difficult to be orthogonal. While for a uniform design, it usually has good space-filling properties, but does not necessarily have small or zero correlations between factors. In this paper, we construct a class of column-orthogonal and nearly column-orthogonal designs for computer experiments by rotating groups of factors of orthogonal arrays, which supplement the designs for computer experiments in terms of various run sizes and numbers of factor levels and are flexible in accommodating various combinations of factors with different numbers of levels. The resulting column-orthogonal designs not only have uniformly spaced levels for each factor but also have uncorrelated estimates of the linear effects in first order models. Further, they are 3-orthogonal if the corresponding orthogonal arrays have strength equal to or greater than three. Along with a large factor-to-run ratio, these newly constructed designs are economical and suitable for screening factors for physical experiments.
文摘Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the discretization errors in SEM could be reduced exponentially to machine zero so that the spectral convergence rate can be achieved. Inherited the advantage of FEM, SEM can enhance resolution via both h-type and p-type mesh-refinement. A penalty method was utilized to compute force fields in particulate flows involving freely moving rigid particles. Results were analyzed and comparisons were made;therefore, this penalty-implemented SEM was proven to be a viable method for two-phase flow problems.
