《数值计算方法》课后题答案(湖南大学出版社(12)

湖南大学出版社《数值计算方法》课后题答案

14

习题三

1．1分别用高斯消元法和列选主元法解方程组（精确到小数点后四位）：

123

123

123

0.26410.17350.86420.7521

0.94110.01750.14630.6310

0.86410.42430.07110.2501

x x x

x x x

x x x

++=-

⎧⎫

⎪⎪

-+=

⎨⎬

⎪⎪

--+=

⎩⎭

解：高斯消元法：

()

0.26410.17350.86420.7521

|0.94110.01750.14630.6310

0.86410.42430.0710.2501

A b

-

⎛⎫

⎪

=-

⎪

⎪

--

⎝⎭

=

0.2641 0.1735 0.8642 -0.7521

0 -0.6358 -2.9332 3.3111

0 0.1434 2.8986 -2.2107

⎛⎫

⎪

⎪

⎪

⎝⎭

0.2641 0.1735 0.8642 -0.7521

0 -0.6358 -2.9332 3.3111

0 0 2.2372 -1.4640

⎛⎫

⎪

= ⎪

⎪

⎝⎭

T

( 0.7315, -2.1889, -0.6544)

x=

高斯列选主元消元法

()

0.26410.17350.86420.7521

|0.94110.01750.14630.6310

0.86410.42430.0710.2501

A b

-

⎛⎫

⎪

=-

⎪

⎪

--

⎝⎭

0.94110.01750.14630.6310

0.26410.17350.86420.7521

0.86410.42430.0710.2501

-

⎛⎫

⎪

=-

⎪

⎪

--

⎝⎭

0.9411 -0.0175 0.1463 0.6310

0 0.1784 0.8231 -0.9292

0 -0.4404 0.2054 0.8295

⎛⎫

⎪

= ⎪

⎪

⎝⎭

0.94110.01750.14630.6310

0 -0.4404 0.2054 0.8295

0 0.1784 0.8231 -0.9292

-

⎛⎫

⎪

= ⎪

⎪

⎝⎭

0.9411-0.01750.1463

0-0.44040.20540.8295

000.9064-0.

5931

⎛⎫

⎪

= ⎪

⎪

⎝⎭

()

x=0.7315, -2.1889,-0.6544 T

2．分别用高斯消元法和列选主元法解方程组