?3.2?1.6???1.0?3.2?1.6???1.0?1.52.54.1?1.52.54.10.50.5??x1??0.90???????1.0x2?1.55
??????1.5????x3????2.08?? 解：
?1.0?1.50.90??1.55
?2.08???1.53.250.5?1.25?1.656250.5?1.250.10096??1.1?1.79875??0.900.90
?3.2???????0???0r2?0.5r1r3-0.3125r1
4.56875?1.53.250?3.2r3-1.40577r2???????0???0??1.1?0.25240??
x3?0.25240
0.10096?2.5
x2?(1.1?1.25?2.5)?3.25?1.3
x1?(0.90?1.5?1.3?0.5?2.5)3.2?0.5 6.用追赶法求解三对角方程组 2.0000M0.3571M0?1.0000M1
?5.5200
20?2.0000M1?0.6429M0.6000M1?2.0000M0.4286M ?4.3144
?0.4000M3
2 ?3.2661
4
2?2.0000M3?0.5714MM3?2.0000M?2.4287?2.1150
1.0000431
解：
?2.0000?0.3571??????0.35712.00000.6000r1r2r3r41.00002.00000.60000.64292.00000.42860.40002.00001.0000?2.0000?0??0??0??01.00001.821450000.64291.78822000.40001.9041300.57142.00005.5200??4.3144?3.2661?
?2.4287?2.1150??5.5200??3.32880?2.16957??1.90870?1.11260??r2?r3?r4?r5? 1.821450.42861.788221.00001.90413
0.57141.69992 等价三角方程组
2.0000M0?1.0000M1 ?5.5200
1.82145M1?0.6429M1.78822M2 ?3.3288 0?0.4000M3
2 ?2.16957
41.90413M3?0.5714M1.69992M?1.90870?1.11260
4 回代得
M4?1.11260M3?M21.69992?0.654501
1.90413?0.80599(1.90870?0.5714?0.654501)(2.1695?0.4000?0.80599)
?1.032971.78822(3.32880?0.6429?1.03297)M1??1.462961.821450?
M?(5.5200?1.0000?1.46296)2.0000?2.02852
?M0?2.0285，M1?1.4630，M2?1.0330，
M3?0.8060,
M4?0.6545
32
试用列主元Gauss消去法解下列方程组：
?121??x?1??3??340????x???2???3? ??2104????x3????10???1213??34
解：A???3403???r?1???r2???12??210410????210r12?r1??3?r?23403???3?3r?1???022?
?31???22??0348??????403??r?2???r3??3?0228?? ?34??2??0312??????r1r3403???3?11??2???022?348?? ???00714??1111?? 等价三角方程组
3x1?4x2
?3
223x2?4x3?8
71411x3?11
x3?2，x2?0，x1?1
33
03?13??410??9. 11. 设计算机具有4位字长。分别用Gauss消去法和列主元Gauss消去法解
下列方程组，并比较所得的结果。 x?592y?437 592x?4308y?2251 解： Gauss消去法
?1A???592r?592r5924308439?0.1000?101??2251?0.592?1030.5920?100.4308?10340.439?10340.2251?10
21?????
?0.1000?101?0??0.1000?101??0??0.1000?101??0?0.5920?1043320.4308?10?(0.5920?10)0.5920?10436? 46?0.2251?10?0.592?0.439?10?0.439?100.439?10330.4308?10?0.3505?100.592?1036? 46?0.2251?10?0.2560?10?3
?0.3462?10?6??0.2574?10?0.439?10
回代
y?(?0.2574?10)?(?0.3462?10)?0.7435?10330660
1x?[0.4390?10?(0.592?10)?(0.7435?10)]?(0.1000?10)
?(0.4390?0.4402)?103??0.1200?101 列主元Gauss消去
?592A???143085922251?? 439??0.5920?103??1?0.1000?100.5390?10????????r2?1r310.4308?100.5920?104340.2251?10? 3?0.4390?10?
34
?0.5920?103?0?0.0000?10?0.4308?1040.4308?1030.5920?10?30.5920?1040.2251?1040.2251?1030.4390?10?30.5390?104????
?0.5920?103??0?0.4308?103410.5920?10?0.7277?10? 31?0.4390?10?0.4176?10?0.2251?104?0.5920?103??0.4308?1040.2251?104??00.5217?1030.4348?103? ?y?0.8334?100
x??0.2262?101
15. 用列主元三角分解法求解方程组。其中
?121?2??A=?253?2????2?235?, ??1323??
解：
?121?24??
A??253?27????2?235?1? ??13230???253?27?? ?121?24????2?235?1?
??13230??35
?4???b??7???1? ??0??