Description: This book aims to give a general overview of the theoretical foundations of
learning theory. It is not the rst to do so.Yet we wish to emphasize a viewpoint
that has drawn little attention in other expositions, namely, that of approximation
theory. This emphasis fullls two purposes. First, we believe it provides a
balanced view of the subject. Second, we expect to attract mathematicians
working on related elds who nd the problems raised in learning theory close
to their interests. Platform: |
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Description: 本文首先介绍了粗糙集理论的基本概念，包括等价关系、不可分辨关系、上下近似、粗糙集和简约；并且从空间数据挖掘、遥感影像处理、GIS 不确定性、GIS 数据分析、模糊地理对象建模和粗糙集与其它软计算方法的结合等六方面概述了粗糙集理论在GIS 数据处理中应用的进展-This paper introduces the basic concepts of rough set theory, including the equivalence relation, can not distinguish between lower and upper approximation, Rough sets and simple and from spatial data mining, remote sensing image processing, GIS uncertainty, GIS data analysis, fuzzy geographical objects Modeling and rough sets and other soft computing methods outlined six aspects such as the combination of rough set theory in GIS progress in the application of data processing Platform: |
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Author:胡伟 |
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Description: 本文首先介绍了粗糙集理论的基本概念，包括等价关系、不可分辨关系、上下近似、粗糙集和简约；并且从空间数据挖掘、遥感影像处理、GIS 不确定性、GIS 数据分析、模糊地理对象建模和粗糙集与其它软计算方法的结合等六方面概述了粗糙集理论在GIS 数据处理中应用的进展-This paper introduces the basic concepts of rough set theory, including the equivalence relation, can not distinguish between lower and upper approximation, Rough sets and simple and from spatial data mining, remote sensing image processing, GIS uncertainty, GIS data analysis, fuzzy geographical objects Modeling and rough sets and other soft computing methods outlined six aspects such as the combination of rough set theory in GIS progress in the application of data processing Platform: |
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Author:胡伟 |
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Description: 《有限元方法的数学理论》中不但提供有限元法系统的数学理论。还兼重在工程设计和分析中的应用算法效率、程序开发和较难的收敛问题。目次：基本概念；Sobolev空间；椭圆边界值问题变分公式；有限元空间结构；Sobolev空间中的多项式近似理论．n维变分问题；有限元多栅法；加性Schwarz预条件； 极大范数估计；自适应网格； 变分病态、在平面弹性力学中的应用；混合法；迭代技巧用于混合法；算子插值理论的应用。读者对象；数学、物理和工程专业的研究生和技术人员。-" The mathematical theory of finite element method" in the finite element method system not only provides the mathematical theory. And also focuses on engineering design and analysis of efficiency of the algorithm, program development and the convergence problem more difficult. Table of Contents: Basic concepts Sobolev space elliptic boundary value problems variational formulation finite element spatial structure Sobolev space theory of polynomial approximation. n-dimensional variational problem finite element multi-grid method additive Schwarz preconditioner maximum norm estimate adaptive grid pathological variation in the plane elasticity in the application mixed iterative techniques for mixed method Operator Interpolation Theory. Readers mathematics, physics and engineering graduate students and technical staff. Platform: |
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Author:xiangyunl |
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Description: 模擬退火是一種通用概率演算法，用來在固定时间内寻求在一個大的搜尋空間內找到的最優解。
模擬退火來自冶金學的專有名詞退火。退火是將材料加熱後再經特定速率冷卻，目的是增大晶粒的體積，並且減少晶格中的缺陷。材料中的原子原來會停留在使內能有局部最小值的位置，加熱使能量變大，原子會離開原來位置，而隨機在其他位置中移動。退火冷卻時速度較慢，使得原子有較多可能可以找到內能比原先更低的位置。
模擬退火的原理也和金屬退火的原理近似：我們將熱力學的理論套用到統計學上，將搜尋空間內每一點想像成空氣內的分子；分子的能量，就是它本身的動能；而搜尋空間內的每一點，也像空氣分子一樣帶有「能量」，以表示該點對命題的合適程度。演算法先以搜尋空間內一個任意點作起始：每一步先選擇一個「鄰居」，然後再計算從現有位置到達「鄰居」的機率。
可以證明，模擬退火演算法所得解依機率收斂到全局最優解。
-Simulated annealing is a generic probabilistic algorithm used in a fixed period of time to seek in a large search space to find the optimal solution.
Simulated annealing terminology from metallurgical annealing. Heating the material after annealing is cooled at a specific rate through the purpose is to increase the grain size, and reduce defects in the crystal lattice. Atoms in the original material will remain in the internal energy of a local minimum position, heating energy increases, atoms leave the original position, and move randomly in other locations. Annealing cooling rate is slow, so that atoms are more likely to be found within a position lower than the original.
The principle is also simulated annealing and metal annealing approximation principle: We will apply the theory of thermodynamics to statistical would imagine every point within the search space of air molecules molecular energy is the kinetic energy of its own while searching for space every point, like air Platform: |
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Description: 函数论的一个重要组成部分，涉及的基本问题是函数的近似表示问题。在数学的理论研究和实际应用中经常遇到下类问题：在选定的一类函数中寻找某个函数g，使它是已知函数?在一定意义下的近似表示，并求出用g近似表示 ?而产生的误差。这就是函数逼近问题。在函数逼近问题中，用来逼近已知函数?的函数类可以有不同的选择；即使函数类选定了，在该类函数中用作?的近似表示的函数g的确定方式仍然是各式各样的；g对?的近似程度（误差）也可以有各种不同的含义。所以函数逼近问题的提法具有多样的形式，其内容十分丰富。(An important part of the functional theory involves the basic problem of the approximate representation of functions. Such problems often encountered in theoretical research and practical application of mathematics in search of a G function in a class of functions selected, it is known that the function f more approximate in some sense representation, and gives the representation f more using the G approximation error and produce. This is the function approximation problem. In function approximation, used to approximate the given function f more functions can have different choices; even if the function is selected, in this kind of function is used as the approximate representation of the function f more G is still the way to determine the approximate degree of every kind of G; the f more (error) can also have various meanings. Therefore, the formulation of the function approximation problem has various forms, and its content is very rich.) Platform: |
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