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1.
Convex Quadratic Approximation   总被引:3,自引:0,他引:3  
For some applications it is desired to approximate a set of m data points in n with a convex quadratic function. Furthermore, it is required that the convex quadratic approximation underestimate all m of the data points. It is shown here how to formulate and solve this problem using a convex quadratic function with s = (n + 1)(n + 2)/2 parameters, s m, so as to minimize the approximation error in the L 1 norm. The approximating function is q(p,x), where p s is the vector of parameters, and x n. The Hessian of q(p,x) with respect to x (for fixed p) is positive semi-definite, and its Hessian with respect to p (for fixed x) is shown to be positive semi-definite and of rank n. An algorithm is described for computing an optimal p* for any specified set of m data points, and computational results (for n = 4,6,10,15) are presented showing that the optimal q(p*,x) can be obtained efficiently. It is shown that the approximation will usually interpolate s of the m data points.  相似文献
2.
基于基样条局部逼近散乱数据拟合中的Shepard方法   总被引:3,自引:1,他引:2       下载免费PDF全文
本文针对散乱数据拟合的shepard方法,提出了一种局部逼近的新方法.该方法以局部三次基样条函数作为Shepard公式中的权函数,新的权函数具有良好的衰减性和二阶连续性,从而改进了传统方法的不足之处,使实际应用效果更好.  相似文献
3.
Least squares data fitting with implicit functions   总被引:2,自引:0,他引:2  
This paper discusses the computational problem of fitting data by an implicitly defined function depending on several parameters. The emphasis is on the technique of algebraic fitting off(x, y; p) = 0 which can be treated as a linear problem when the parameters appear linearly. Various constraints completing the problem are examined for their effectiveness and in particular for two applications: fitting ellipses and functions defined by the Lotka-Volterra model equations. Finally, we discuss geometric fitting as an alternative, and give examples comparing results.  相似文献
4.
几种基于散乱数据拟合的局部插值方法   总被引:1,自引:0,他引:1       下载免费PDF全文
本文首先针对散乱数据拟合的Shepard方法,结合截断多项式、B样条基函数和指数函数来构造其权函数,使新的权函数具有更高的光滑度和更好的衰减性,并且其光滑性和衰减性可以根据实际需要自由调节,从而提高了曲面的拟合质量.同时还给出一种类似的局部插值方法.另外,本文还基于多重二次插值,结合多元样条的思想,给出了两个局部插值算法.该算法较好地继承了多重二次插值曲面的性质,从而保证了拟合曲面具有好地光顺性和拟合精度.曲面整体也具有较高的光滑性.  相似文献
5.
NURBS曲线曲面拟合数据点的迭代算法   总被引:1,自引:0,他引:1       下载免费PDF全文
本文推广了文献[1]的结果,将文献[1]中关于B样条曲线曲面拟合数据点的迭代算法推广至有理形式,给出了无需求解方程组反求控制点及权因子即可得到拟合NURBS曲线曲面的迭代方法.该算法和文献[1]的算法本质上是统一的,而后者恰是前者的一种退化形式.文章还给出了收敛性证明以及一些定性分析.文末的数值实例说明该算法简单实用.  相似文献
6.
数据拟合函数的加权最小二乘积分法   总被引:1,自引:0,他引:1  
数据拟合的方法很多,每种方法各有特点.探讨了积分准则下的数据加权拟合函数的方法,称为加权最小二乘积分法,并给出了三个常用拟合函数具体形式.  相似文献
7.
中央空调系统节能设计   总被引:1,自引:0,他引:1  
根据商场的冷负荷平衡公式,求得商场的平均客流量;利用数据拟合、插值等算法对商场的逐时客流量进行了优化,并建立了以人流量和外部环境温度为变量的商场冷负荷模型;采用模糊控制策略建立了保持商场内部温度稳定的数学模型,可以实现对中央空调系统供冷量的逐时控制;运用微积分原理建立了基准冷负荷的数学模型,为直接基于基准能耗的控制策略提供了可行性依据.  相似文献
8.
Based on the definition of MQ-B-Splines, this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details. And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.  相似文献
9.
Univariate cubic L 1 smoothing splines are capable of providing shape-preserving C 1-smooth approximation of multi-scale data. The minimization principle for univariate cubic L 1 smoothing splines results in a nondifferentiable convex optimization problem that, for theoretical treatment and algorithm design, can be formulated as a generalized geometric program. In this framework, a geometric dual with a linear objective function over a convex feasible domain is derived, and a linear system for dual to primal conversion is established. Numerical examples are given to illustrate this approach. Sensitivity analysis for data with uncertainty is presented. This work is supported by research grant #DAAG55-98-D-0003 of the Army Research Office, USA.  相似文献
10.
We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n 2) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.  相似文献
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