| 查看: 3334 | 回复: 39 | ||||
| 【奖励】 本帖被评价33次，作者laosam280增加金币 26 个 | ||||
[资源]
Orthogonal Polynomials: Computation and Approximation
|
||||
|
关于正交多项式在计算中的应用于方法论CONTENTS Preface viii 1 Basic Theory 1 1.1 Orthogonal polynomials 1 1.1.1 Definition and existence 1 1.1.2 Examples 4 1.2 Properties of orthogonal polynomials 6 1.2.1 Symmetry 6 1.2.2 Zeros 7 1.2.3 Discrete orthogonality 8 1.2.4 Extremal properties 8 1.3 Three-term recurrence relation 10 1.3.1 Monic orthogonal polynomials 10 1.3.2 Orthonormal polynomials 12 1.3.3 Christoffel–Darboux formulae 14 1.3.4 Continued fractions 15 1.3.5 The recurrence relation outside the support interval 17 1.4 Quadrature rules 20 1.4.1 Interpolatory quadrature rules and beyond 21 1.4.2 Gauss-type quadrature rules 22 1.5 Classical orthogonal polynomials 26 1.5.1 Classical orthogonal polynomials of a continuous variable 27 1.5.2 Classical orthogonal polynomials of a discrete variable 32 1.6 Kernel polynomials 35 1.6.1 Existence and elementary properties 36 1.6.2 Recurrence relation 38 1.7 Sobolev orthogonal polynomials 40 1.7.1 Definition and properties 41 1.7.2 Recurrence relation and zeros 41 1.8 Orthogonal polynomials on the semicircle 43 1.8.1 Definition, existence, and representation 43 1.8.2 Recurrence relation 45 1.8.3 Zeros 47 1.9 Notes to Chapter 1 49 v vi CONTENTS 2 Computational Methods 52 2.1 Moment-based methods 52 2.1.1 Classical approach via moment determinants 52 2.1.2 Condition of nonlinear maps 55 2.1.3 The moment maps Gn and Kn 57 2.1.4 Condition of Gn : μ 7! 59 2.1.5 Condition of Gn : m 7! 64 2.1.6 Condition of Kn : m 7! 70 2.1.7 Modified Chebyshev algorithm 76 2.1.8 Finite expansions in orthogonal polynomials 78 2.1.9 Examples 82 2.2 Discretization methods 90 2.2.1 Convergence of discrete orthogonal polynomials to continuous ones 90 2.2.2 A general-purpose discretization procedure 93 2.2.3 Computing the recursion coefficients of a discrete measure 95 2.2.4 A multiple-component discretization method 99 2.2.5 Examples 101 2.2.6 Discretized modified Chebyshev algorithm 111 2.3 Computing Cauchy integrals of orthogonal polynomials 112 2.3.1 Characterization in terms of minimal solutions 112 2.3.2 A continued fraction algorithm 113 2.3.3 Examples 116 2.4 Modification algorithms 121 2.4.1 Christoffel and generalized Christoffel theorems 122 2.4.2 Linear factors 124 2.4.3 Quadratic factors 125 2.4.4 Linear divisors 128 2.4.5 Quadratic divisors 130 2.4.6 Examples 133 2.5 Computing Sobolev orthogonal polynomials 138 2.5.1 Algorithm based on moment information 139 2.5.2 Stieltjes-type algorithm 141 2.5.3 Zeros 143 2.5.4 Finite expansions in Sobolev orthogonal polynomials 146 2.6 Notes to Chapter 2 148 3 Applications 152 3.1 Quadrature 152 3.1.1 Computation of Gauss-type quadrature formulae 152 CONTENTS vii 3.1.2 Gauss–Kronrod quadrature formulae and their computation 165 3.1.3 Gauss–Tur´an quadrature formulae and their computation 172 3.1.4 Quadrature formulae based on rational functions 180 3.1.5 Cauchy principal value integrals 202 3.1.6 Polynomials orthogonal on several intervals 207 3.1.7 Quadrature estimation of matrix functionals 211 3.2 Least squares approximation 216 3.2.1 Classical least squares approximation 217 3.2.2 Constrained least squares approximation 221 3.2.3 Least squares approximation in Sobolev spaces 225 3.3 Moment-preserving spline approximation 227 3.3.1 Approximation on the positive real line 228 3.3.2 Approximation on a compact interval 237 3.4 Slowly convergent series 239 3.4.1 Series generated by a Laplace transform 240 3.4.2 “Alternating” series generated by a Laplace transform 245 3.4.3 Series generated by the derivative of a Laplace transform 246 3.4.4 “Alternating” series generated by the derivative of a Laplace transform 248 3.4.5 Slowly convergent series occurring in plate contact problems 249 3.5 Notes to Chapter 3 253 Bibliography 261 Index 283 [ Last edited by feixiaolin on 2014-1-5 at 07:27 ] |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com - 附件 1 : Orthogonal_Polynomials_Computation_and_Approximation.pdf
2014-01-04 23:56:21, 3.84 M
» 收录本帖的淘帖专辑推荐
 计算数学 | 数学 |
» 猜你喜欢
308求调剂
已经有4人回复
-
NSFC申报书里申请人简历中代表性论著还需要在申报书最后的附件里面再上传一遍吗
已经有14人回复
-
材料与化工一志愿南昌大学327求调剂推荐
已经有6人回复
-
化学调剂0703
已经有7人回复
-
327求调剂
已经有11人回复
-
调剂
已经有8人回复
-
梁成伟老师课题组欢迎你的加入
已经有7人回复
-
伙伴们，祝我生日快乐吧
已经有24人回复
-
中科院材料273求调剂
已经有3人回复
-
材料工程专硕274一志愿211求调剂
已经有5人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- C数值算法程序大全
已经有7人回复
5楼2014-01-08 15:24:19
6楼2014-01-09 12:05:33
|
本帖内容被屏蔽 |
7楼2014-01-09 12:22:08
15楼2014-06-25 22:20:39
17楼2014-08-07 10:58:44
18楼2014-09-01 17:01:31
19楼2014-09-11 10:55:54
，我是新虫38楼2018-10-05 08:09:54
39楼2018-10-05 08:15:23
简单回复
tryhard2楼
2014-01-06 17:24
回复
五星好评 顶一下，感谢分享！
2014-01-06 21:38
回复
五星好评 顶一下，感谢分享！
applaq4楼
2014-01-07 08:26
回复
五星好评 顶一下，感谢分享！
2014-01-20 01:27
回复
顶一下，感谢分享！
hi_next9楼
2014-01-25 11:03
回复
五星好评 顶一下，感谢分享！
Junehall10楼
2014-01-28 15:39
回复
五星好评 顶一下，感谢分享！
gcadam11楼
2014-03-04 21:45
回复
五星好评 顶一下，感谢分享！
12hgh12楼
2014-03-24 21:59
回复
五星好评 顶一下，感谢分享！
doufu57213楼
2014-04-18 21:40
回复
五星好评 顶一下，感谢分享！
happymind14楼
2014-05-21 12:39
回复
五星好评 顶一下，感谢分享！
kabaisun16楼
2014-07-23 08:28
回复
五星好评 顶一下，感谢分享！
iloveorc52120楼
2014-09-12 14:29
回复
五星好评 顶一下，感谢分享！
dearyx21楼
2014-11-18 10:50
回复
五星好评 顶一下，感谢分享！
wangth092122楼
2014-11-18 11:26
回复
五星好评 顶一下，感谢分享！
m06z51123楼
2014-11-19 08:52
回复
五星好评 顶一下，感谢分享！
chailei24楼
2014-11-28 21:02
回复
五星好评 顶一下，感谢分享！
玄念25楼
2014-11-29 21:29
回复
五星好评 顶一下，感谢分享！
copwht26楼
2014-12-09 14:14
回复
五星好评 顶一下，感谢分享！
lirumei127楼
2015-02-17 14:19
回复
五星好评 顶一下，感谢分享！
seesea28楼
2016-03-28 15:03
回复
五星好评 顶一下，感谢分享！
askuyue29楼
2016-09-27 20:18
回复
五星好评 顶一下，感谢分享！
happytik30楼
2016-09-28 22:39
回复
顶一下，感谢分享！
曼166531楼
2017-04-21 08:31
回复
五星好评 顶一下，感谢分享！
wangth092132楼
2017-04-21 10:21
回复
顶一下，感谢分享！
eyespike33楼
2017-09-26 11:42
回复
五星好评 顶一下，感谢分享！
zhanggen03634楼
2017-10-11 15:19
回复
五星好评 顶一下，感谢分享！
xmujiali35楼
2017-10-24 14:41
回复
五星好评 顶一下，感谢分享！
罗代均36楼
2018-06-09 09:50
回复
五星好评 顶一下，感谢分享！
andizhai37楼
2018-06-10 18:57
回复
五星好评 顶一下，感谢分享！
wwhblue40楼
2019-08-13 16:54
回复
五星好评 顶一下，感谢分享！
