数值分析 课件 chapter1

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1、ê©ÛØÄVg(NumericalAnalysis)êâØé¼êK{ê½5¢SO¥A5¿...SK¯ÌIKJJIIÇ÷JIÀHÆêÆX11
25£hwwu@seu.edu.cn¶w«'4òÑ8¹ØÄVgêâØé¼êK{ê½51XØ¢SO¥A5¿...25§¦SK35§

2、ê)¯ÌIK4%CJJII5êÈ©Úê©JI6~©§ê)12
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3、ringer-Verlag,.ãÖSKÑúi,2003.¯Ì2.DavidKincaid,WardCheney.ê©Û.ÅóÑ,IK2003.JJII3.o,U,´Â.ê©Û.u¥EÆÑ,JI1986.13
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4、ØÙÌSNØÄVg1)ØVgêâØé¼êKýéØ()!éØ()!kêi9§m'X{ê½52)êâØé¼êK¢SO¥A5¿...?ؼêØgCþØm'XSK3){ê½5¯Ì?ØЩêâØéO(JKIK4)¢SO¥A5¿¯KJJIIJI15
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25£¶w«'4òÑ1.2ýéؽ½½ÂÂÂ1x∗O(,x´x∗Cq.PØÄVge(x)=x

5、∗−x,êâØé¼êK{ê½5¡e(x)CqxýéØ.¢SO¥A5¿...ýéئØÑ,Ï°(x∗Ø.3¢S¯K¥,SKØÒ1.XJ∃ε>0,¦¯Ì∗

6、e(x)

7、=

8、x−x

9、≤ε,IKKε¡CqxýéØ,k±L«¤x∗=x±ε.JJIIJI17
25£¶w«'4òÑ1.3éؽ½½ÂÂÂ2x∗O(,x´x∗Cq.PØÄVg∗x−xe(x)êâØé¼êKer(x)==,x∗x∗{ê½5K¡e(x)CqxéØ.¢SO¥A5¿...rSKdu°(x∗J±¦,Ï~±¯Ìx∗−xe¯r(x)=IKxJJIIxéØ.

10、XJ∃ε,¦JIr

11、e(x)

12、≤ε½

13、e¯(x)

14、≤ε,18
25rrrr£Kεr¡xéØ.¶w«'4òÑ1.4kê½½½ÂÂÂ3XJCqxýéØ´Ù,ü,ØÄVgTx1"êim
kn,K¡xäknkêâØé¼êKêi,^ùnkêiL«Cqê¡kê.{ê½5¢SO¥A5¿...XπCqx1=3.14,KSK1−2

15、π−x1

16、=0.00159···<0.005=×10,¯Ì2IK¤±x1k3kêi;Xx2=3.1416,K1JJII−4

17、π−x2

18、<0.00005=×10,2JI¤±xk5kêi;Xx

19、=3.1415,K19
25231£−3

20、π−x3

21、=0.00009···<0.0005=×10,2¶w«¤±x3k4kêi.'4òÑ2êâØé¼êKx∗,x∗O(,y∗=f(x∗,x∗),x,xéACq,y=121212ØÄVgf(x1,x2).d¼êTaylorÐmêâØé¼êKe(y)=y∗−y=f(x∗,x∗)−f(x,x){ê½51212∂f(x,x)∂f(x,x)¢SO¥A5¿...12∗12∗≈(x1−x1)+(x2−x2),SK∂x1∂x2=¯Ì∂f(x,x)∂f(x,x)IK1212e(y)≈e(x1

22、)+e(x2).(1)∂x∂xJJII12l±JIe(y)∂f(x,x)x110
25121er(y)=≈er(x1)y∂xf(x,x)£112∂f(x1,x2)x2¶w«+er(x2).(2)∂x2f(x1,x2)'4òÑ

23、^(1)Ú(2)±e(x1+x2)=e(x1)+e(x2),(3)ØÄVge(x1−x2)=e(x1)−e(x2),(4)êâØé¼êKe(x1x2)≈x2e(x1)+x1e(x2),(5){ê½5ex1≈1e(x)−x1e(x),(6)¢SO¥A5¿...xx1x22222SKx1x2er(x1+

24、x2)≈er(x1)+er(x2),(7)¯Ìx1+x2x1+x2x1x2IKer(x1−x2)≈er(x1)−er(x2),(8)x1−x2x1−x