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求解线性和非线性方程组的Kaczmarz类方法
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  • ISBN:
    9787511468307
  • 作      者:
    李维国,邢丽丽,鲍文娣,乔田田
  • 出 版 社 :
    中国石化出版社
  • 出版日期:
    2022-08-01
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作者简介

李维国,博士,教授,博士生导师,1997年12月毕业于南京大学计算数学专业,获博士学位。2000年11月被聘为中国石油大学(华东)数学系教授至今,现为中国石油大学(华东)博士生导师、理学院教授委员会主任、数学学科负责人。主要从事计算数学和应用数学和力学等方面的研究工作。

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精彩书摘

 

29 A Note: Minimum-Norm Solution of Least Square Problem  117
210 RK or RGS for Ridge Regression 119
211 Randomized Block Kaczmarz Method   124
212 Randomized Block CD Method  128
213 Randomized Double Block Kaczmarz Method131
2131 RDBK with Pseudoinverse132
2132 Pseudoinverse-Free RDBK 133
3 Sparse Kaczmarz-Type Methods  144
31 Sparse Solution and Sparse Least Square Solution 144
32 Iterative Hard Thresholding Based on RK152
33 Iterative Soft Thresholding Based on RK154
4 Nonlinear Kaczmarz-Type Methods and Its Variants 162
41 Landweber-Kaczmarz-Type Iteration 163
411 Landweber Iteration163
412 Landweber-Kaczmarz (LK) Iteration163
413 Stochastic Gradient Descent Method165
414 Loping Landweber-Kaczmarz (LLK) Method168
415 Embedded Landweber-Kaczmarz (ELK) Method168
416 Loping Steepest-Descent-Kaczmarz Method (LSDK)170
417 Regularizing Newton-Kaczmarz Method  170
418 Loping LM-Kaczmarz (LLMK) method173
419 Averaged Kaczmarz (AVEK) Method 173
42 Nonlinear Randomized Kaczmarz Method 176
43 NK and NURK 182
44 Nonlinear Coordinate Descent Method 190
45 Nonlinear Uniformly Randomized CD Method 192
46 Nonlinear Maximal Residual Kaczmarz Method192
47 Nonlinear GRK194
5 Kaczmarz-Type Methods in Other Problems  197
51 Learning Theory for Kaczmarz Methods 197
511 Learning Theory for RK 197
512 Learning Theory for Sparse RK 201
52 Kaczmarz Methods for Linear Inequalities203
53 Other Issues206

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目录

1 Kaczmarz Method and Its Variants 1
11 Algebraic Reconstruction Technique 1
111 Kaczmarz Method 1
112 The Simultaneous Iteration Reconstruction Technique    5
12 Coordinate Descent Method 9
13 Maximal Correction Kaczmarz Method 12
131 MCK For Linear Problem 12
132 Finite Termination of MCK Method14
14 Kaczmarz Method with Oblique Projection  15
15 Coordinate Descent Method with Oblique Direction  25
16 General Oblique Projection Method27
17 Block Kaczmarz Method and Block CD Method 35
18 Greedy Block Kaczmarz Method 36
19 Greedy Block Gauss-Seidel Method 41
2 Random Kaczmarz Method and Its Variants 46
21 Random Kaczmarz Method46
22 New Random Kaczmarz Method for 51
23 New Random Kaczmarz Method for  55
24 Greedy Randomized Kaczmarz Method 63
25 RGS and GRGS 68
26 REK and REGS 77
27 RK and RGS with Oblique Projection81
271 Random Kaczmarz Method with Oblique Projection   81
272 RGS with Oblique Projection86
273 GRK and GRGS with Oblique Projection  90
274 Maximal Weighted Residual KO and GSO Methods 96
28 Residua-Based REK100
281 Partially Randomized Extended Kaczmarz Method with Residuals  101
282 Maximum-distance Extended Kaczmarz Method  113

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