数值分析(英)复习提纲
考试以基本概念为主,书上以前布置的计算机题目都不作要求。
第一章Solving equations
1.1 THE BISECTION METHOD
(a) 熟练掌握二分法;
(b) 对于给定解的误差精度要求能够熟练计算所需二分法步数,参考书上28页内容。
习题5,6
1.2 FIXED-POINT ITERATION
(a) 熟练掌握不动点迭代方法求方程的根;掌握不动点迭代方法的线性收敛性与收敛率; 此节书后习题不作要求。
1.4 NEWTON’S METHOD
(a)熟练掌握方程求根的NEWTON’S METHOD:Example 1.11, 1.12, 1.13
(b)对于重根熟练掌握Theorem 1.12, Theorem 1.13
习题2,5,7
第二章Systems of Equations
2.2 THE LU FACTORIZATION
(a)掌握矩阵LU分解方法;
(b)会使用LU分解方法求线性方程组的解:Example 2.5, 2.6, 2.7
2.3 SOURCES OF ERROR
本节只要掌握矩阵范数的定义,参阅90页
2.4 THE PA = LU FACTORIZATION
熟练掌握2.4.2 Permutation matrices, 2.4.3 PA = LU factorization: Example 2.16, 2.17, 2.18
习题4
2.5 ITERATIVE METHODS
熟练掌握Jacobi Method,Gauss–Seidel Method. 习题2
第三章Interpolation
3.1 DATA AND INTERPOLATING FUNCTIONS:
(a)熟练掌握Lagrange interpolation
(b)熟练掌握Newton’s divided differences
习题1,2,5
3.2 INTERPOLATION ERROR
熟练掌握定理3.4, Example 3.8, 习题1,2,4
第四章Least Squares
4.1.1 Inconsistent systems of equations
熟练掌握Normal equations for least squares:Example 4.1, Example 4.2
习题1,2
第五章Numerical Differentiation and Integration
5.1 NUMERICAL DIFFERENTIATION
熟练掌握一阶导数的Two-point forward-difference formula,Three-point centered-difference formula
熟练掌握二阶导数的Three-point centered-difference formula for second derivative
习题1,2,5,8,9
5.2 NEWTON–COTES FORMULAS FOR NUMERICAL INTEGRATION
熟练掌握Composite Trapezoid Rule,Example 5.8,习题1
第六章Ordinary Differential Equations
6.1.1 Euler’s Method
(a) 熟练掌握Euler方法(6.7): Example6.2 习题5
6.2.2 The explicit Trapezoid Method
熟练掌握The explicit Trapezoid Method(6.29):Example6.10 习题1。