数值分析 chapter1new

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1、ØÄVgêâØé¼êKê©Û{ê½5¢SO¥A5¿...(NumericalAnalysis)SK¯ÌIKJJIIÀHÆêÆXOêÆï¿JI<:Ç÷9Ï:§ùN11
24£¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,2011ØÄVgêâØé¼êK8¹{ê½5¢SO¥A5¿...1XØSK25§¦¯Ì35§

2、ê)IKJJII4%CJI5êÈ©Úê©12
246~©§ê)£7©§ê)¶w«'4òÑDepartmentofMathematics,SoutheastU

3、niversity,2011ë]ØÄVgêâØé¼êK1.§,¤²,ªÐ.ê©Û(1n).ÀHÆÑ{ê½5¢SO¥A5¿...,2011.(§á)SK2.RainerKress.NumericalAnalysis.Springer-Verlag,.ãÖ¯ÌÑúi,2003.IK3.DavidKincaid,WardCheney.ê©Û.ÅóÑ,JJII2003.JI4.o,U,´Â.ê©Û.u¥EÆÑ,13
241986.£5.§,Ç÷,ùN.ê©ÛýÁK)Û(2007-2012).¶w«ÀHÆÑ,2012.'4òÑDepa

4、rtmentofMathematics,SoutheastUniversity,2011ØÄVgþÅSKêâØé¼êK{ê½5±eþÅK8À5,U?¦J.¢SO¥A5¿...1Ùp.2017SK1Ùp.5620¯Ì1nÙp.126-12739,40IK1oÙp.19537JJII1ÊÙp.25623JI18Ùp.3072314
241ÔÙp.34610£¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,20111ÙXØÙÌSNØÄVg1)ØVgêâØé¼êKýéØ()!éØ()!k

5、êi9§m'X{ê½52)êâØé¼êK¢SO¥A5¿...?ؼêØgCþØm'XSK3){ê½5¯Ì?ØЩêâØéO(JKIK4)¢SO¥A5¿¯KJJIIJI15
24£¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,20111ØÄVg1.1ýéØØÄVgêâØé¼êK½½½ÂÂÂ1x∗O(,x´x∗Cq.P{ê½5∗e(x)=x−x,¢SO¥A5¿...SK¡e(x)CqxýéØ.¯Ì3¢SO¥,ýéØÃ{¦Ñ(Ï°(x∗).ýIKõê¹e,IØ.XJ

6、∃ε>0,¦JJII∗

7、e(x)

8、=

9、x−x

10、≤ε,JIKε¡CqxýéØ,k±L«¤x∗=x±ε.16
24£¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,20111.2éؽ½½ÂÂÂ2x∗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.XJ∃ε,¦JIr

11、e(x)

12、≤ε½

13、e¯(x)

14、≤ε,17
24rrrr

15、£Kεr¡xéØ.¶w«'4òÑDepartmentofMathematics,SoutheastUniversity,20111.3kê½½½ÂÂÂ3XJCqxýéØ´Ù,ü,ØÄVgTx1"êim
kn,K¡xäknkêâØé¼êKêi.XJCq"Ñ´kêi,KÙkê.{ê½5¢SO¥A5¿...XπCqx1=3.14,KSK1−2

16、π−x1

17、=0.00159···<0.005=×10,¯Ì2IK¤±x1k3kêi;Xx2=3.1416,K1JJII−4

18、π−x2

19、<0.00005=×10,2JI¤±xk5kêi;X

20、x=3.1415,K18
24231£−3

21、π−x3

22、=0.00009···<0.0005=×10,2¶w«¤±x3k4kêi.'4òÑDepartmentofMathematics,SoutheastUniversity,20112êâØé¼êKx∗,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)

23、,SK∂x1∂x2=¯Ì