求解线性和非线性方程组的Kaczmarz类方法 Kaczmarz-Type Methods for Solving Linear

本书介绍了线性和非线性方程组求解中的各种 Kaczmarz类算法及其收敛性（率），主要内容包括 按顺序的循环Kaczmarz类方法、随机Kaczmarz类 方法、稀疏Kaczmarz类方法、非线性Kaczmarz类 方法和部分Kaczmarz方法在其他相关问题中的应用 。本书内容详实、推导详细、算法分析全面，对于 应用Kaczmarz类方法求解大规模数学模型问题具有 很好的参考价值。本书为英文著作，可作为大规模 科学与工程计算、机器学习与数据处理、信号与图 像处理等领域的本科生、研究生、博士生的教学用 书，也可作为教学科研一线教师和科研人员的参考 书。

Contents 1 Kaczmarz Method and Its Variants 1.1 Algebraic Reconstruction Technique 1.1.1 Kaczmarz Method 1.1.2 The Simultaneous Iteration Reconstruction Technique 1.2 Coordinate Descent Method 1.3 Maximal Correction Kaczmarz Method 1.3.1 MCK For Linear Problem 1.3.2 Finite Termination of MCK Method 1.4 Kaczmarz Method with Oblique Projection 1.5 Coordinate Descent Method with Oblique Direction 1.6 General Oblique Projection Method 1.7 Block Kaczmarz Method and Block CD Method 1.8 Greedy Block Kaczmarz Method 1.9 Greedy Block Gauss-Seidel Method 2 Random Kaczmarz Method and Its Variants 2.1 Random Kaczmarz Method 2.2 New Random Kaczmarz Method for 2.3 New Random Kaczmarz Method for 2.4 Greedy Randomized Kaczmarz Method 2.5 RGS and GRGS 2.6 REK and REGS 2.7 RK and RGS with Oblique Projection 2.7.1 Random Kaczmarz Method with Oblique Projection 2.7.2 RGS with Oblique Projection 2.7.3 GRK and GRGS with Oblique Projection 2.7.4 Maximal Weighted Residual KO and GSO Methods 2.8 Residua-Based REK 2.8.1 Partially Randomized Extended Kaczmarz Method with Residuals 2.8.2 Maximum-distance Extended Kaczmarz Method 2.9 A Note: Minimum-Norm Solution of Least Square Problem 2.10 RK or RGS for Ridge Regression 2.11 Randomized Block Kaczmarz Method 2.12 Randomized Block CD Method 2.13 Randomized Double Block Kaczmarz Method 2.13.1 RDBK with Pseudoinverse 2.13.2 Pseudoinverse-Free RDBK 3 Sparse Kaczmarz-Type Methods 3.1 Sparse Solution and Sparse Least Square Solution 3.2 Iterative Hard Thresholding Based on RK 3.3 Iterative Soft Thresholding Based on RK 4 Nonlinear Kaczmarz-Type Methods and Its Variants 4.1 Landweber-Kaczmarz-Type Iteration 4.1.1 Landweber Iteration 4.1.2 Landweber-Kaczmarz (LK) Iteration 4.1.3 Stochastic Gradient Descent Method 4.1.4 Loping Landweber-Kaczmarz (LLK) Method 4.1.5 Embedded Landweber-Kaczmarz (ELK) Method 4.1.6 Loping Steepest-Descent-Kaczmarz Method (LSDK) 4.1.7 Regularizing Newton-Kaczmarz Method