西安建筑科技大学：《高等数学计算方法》课程教学资源（PPT课件讲稿）Chapter 2.4 Gaussian Elimination and Pivoting 2.5 Triangular Factorization

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: (1) 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+Bc+Ca- that passes througl the three points(1, 1),(2,-1), and(3,1)

A+B+C=1 at(1, A+2B+4C=-1at(2,-1) 215) A+3B+9C=1at(3,1)

A+B+C 芦+3C=2 26+0=0

A+B+C= 1 芦+C=2

2.5 Trianqular Factorization

2.5 Triangular Factorization

121314 111213214 21022a23a14 22023 4 031a32033a34 m11m732 000 u33134 4142a43a44 m41m742m043 0044

4.5. 1 Solution of a linear syste

4.5.1 Solution of a linear System

4.5.2 Triangular factorization

4.5.2 Triangular Factorization