- 电子工业出版社
- 9787121416521
- 1-2
- 421610
- 47245626-8
- 平塑
- 16开
- 2022-06
- 229
- 176
- 数学
- 本科 研究生（硕士、EMBA、MBA、MPA、博士）
目录
第1章 插值与逼近.......................................................1 1.1 问题介绍..........................................................1 1.2 多项式插值.......................................................2 1.2.1 概述.......................................................2 1.2.2 Lagrange插值..............................................4 1.2.3 Newton插值...............................................6 1.2.4 分片线性插值..............................................8 1.2.5 Hermite插值..............................................10 1.3 径向基函数插值..................................................13 1.3.1 概述......................................................13 1.3.2 再生核空间...............................................16 1.3.3 误差估计..................................................18 1.4 最佳逼近.........................................................20 1.4.1 最小二乘拟合.............................................20 1.4.2 最佳一致逼近.............................................22 1.4.3 最佳平方逼近.............................................23 1.4.4 正交多项式...............................................24 1.5 注记.............................................................26 习题1................................................................27 第2章 数值微分与数值积分.............................................31 2.1 问题介绍.........................................................31 2.2 数值微分.........................................................31 2.2.1 Taylor展开求导...........................................31 2.2.2 插值型求导...............................................33 2.3 数值积分.........................................................35 2.3.1 中点、梯形和Simpson求积公式..........................35 2.3.2 Newton-Cotes求积公式...................................37 2.3.3 复合求积公式.............................................39 2.3.4 Romberg求积公式........................................40 2.3.5 Gauss求积公式...........................................41 2.4 注记.............................................................45 习题2................................................................46 第3章 求解线性方程组..................................................49 3.1 问题介绍.........................................................49 3.2 直接法...........................................................50 3.2.1 LU分解..................................................50 3.2.2 Cholesky分解.............................................52 3.2.3 QR分解..................................................53 3.3 基本迭代法......................................................56 3.3.1 三种基本迭代法...........................................56 3.3.2 收敛性准则...............................................61 3.4 共轭梯度法......................................................62 3.5 注记.............................................................66 习题3................................................................66 第4章 求解非线性方程组...............................................70 4.1 问题介绍.........................................................70 4.2 非线性方程的迭代法.............................................70 4.2.1 二分法....................................................71 4.2.2 不动点迭代...............................................72 4.2.3 Newton迭代..............................................74 4.2.4 割线法....................................................75 4.3 非线性方程组的迭代法...........................................78 4.3.1 基本非线性迭代法.........................................78 4.3.2 Newton迭代法............................................80 4.3.3 Broyden算法.............................................81 4.4 注记.............................................................83 习题4.............................
