《数值分析》课程PPT教学课件（英文版）Chapter 02 Numerical Integration 2.4 Gaussian Elimination and Pivoting

2.4 Gaussian Elimination and Pivoting

2.4 Gaussian Elimination and Pivoting

Theorem 3.7. (Elementary Transformations). The following opera- tions applied to a linear system yield an equivalent system: ()Interchange: The order of two equations can be changed. (2)Scaling: Multiplying an equation by a nonzero constant. (3)Replacement: An equation can be replaced by the sum of itself and a nonzero multiple of any other equation

Example 3. 15. Find the parabola y= A+ B2+Ca- that passes through the three points(1,1), (2, -1), and(3, 1)

A+B+C=1at(1,1) A+2B+4C=-1at(2,-1 (2.15) A+3B+9C=1at(3,1

A+B+C=1 B+3C=2 2B+8C=0

A+B=1 B+3c 20 4

2.5 Triangular Factorization

2.5 Triangular Factorization

11a12a13a14 l1112213t14 021022023a14 m2110002223 031032033034 00 41042a43044 m4m42m431」L000

4.5.1 Solution of a linear system

4.5.1 Solution of a linear System

4.5.2 Triangular Factorization

4.5.2 Triangular Factorization