2012-13年数值分析试题

福建农林大学研究生课程考试卷授课时间20122013学年度第1学期学号1121213004研究生姓名吴翠兰课程名称数值分析考试时间20121225考生成绩授课或主考教师（签章）201213学年1福建农林大学机电学院研究生数值分析课程试卷姓名吴翠兰班级2012级学号1121213004成绩1、用对分区间法求方程在区间1,2上的一个实根。精度02LNXXF要求为。（10分）610【解】/头文件包含区/INCLUDEINCLUDEINCLUDE/定义声明区/INTN0,N0DOUBLEA0,B0,E0,X0VOIDSTEP_1VOIDVOIDSTEP_2VOIDVOIDSTEP_3VOIDVOIDSTEP_4VOIDVOIDSTEP_5VOIDVOIDSTEP_6VOIDVOIDSTEP_7VOID/FX函数/DOUBLEFDOUBLEXDOUBLERESULT/输入FXRESULTXLOGX22RETURNRESULT/子函数/VOIDSTEP_1VOIDDOUBLEFDOUBLEXA1B2E0000001N1000VOIDSTEP_2VOIDN0VOIDSTEP_3VOIDXAB/2VOIDSTEP_4VOIDIFFABSFXINCLUDEINCLUDEDEFINEN3/矩阵阶数3/定义声明区/INTI0,J0,K0,R0FLOATSUM10,SUM20,SUM30,SUM40FLOATAN1N10FLOATLN1N10FLOATUN1N10FLOATBN10FLOATYN10FLOATXN10/主函数/VOIDMAIN/矩阵AIJ/矩阵BK/A112A121A131B14A213A224A232B211A313A322A334B311/求矩阵UJ1KFORJK1JINCLUDEDEFINEN5TYPEDEFSTRUCTDOUBLEXDOUBLEYPOINTDOUBLEPARABOLAPOINT,POINT,POINT,DOUBLEINTMAINDOUBLEX0,Y0INTI0,N0/N为要插的中间那个点的位置CHARCYPOINTPNFORI0IPN2XPN1XNN2ELSENINTN/2/PRINTF“DN“,NYPARABOLAPRINTF“YLFN“,YPRINTF“CONTINUEY/N“SCANF“C“,WHILE10GETCHARCONTINUERETURN0DOUBLEPARABOLAPOINTP1,POINTP2,POINTP3,DOUBLEXDOUBLETEMP10,TEMP20,TEMP30,Y0DOUBLEA0,B0,C0TEMP1P2YP1YXP1XTEMP2P3YP1YP2XP1XP2YP1YP3XP1XTEMP3P3XP1XP3XP1XP2XP1XYP1YTEMP1/P2XP1XTEMP2XP1XXP2X/TEMP3RETURNY调试结果4、对于函数，从X00开始，去步长H01的20个数据点，求5XEXF次最小二乘拟合多项式55443322105XAXAXAXAXAXP其中（即求系数AI,I0,1,5）（10分）950219IX【解】/头文件包含区/INCLUDEINCLUDEINCLUDEDEFINEM5/最小二乘M次拟合多项式5DEFINEN20/数据点的个数20/定义声明区/INTI0,J0,K0,R0DOUBLESUM10,SUM20,SUM30,SUM40DOUBLEAM2M20DOUBLELM2M20DOUBLEUM2M20DOUBLEBM20DOUBLEYM20DOUBLEXM20DOUBLEAM10DOUBLEYN10DOUBLEXN10/主函数/VOIDMAIN/数组XII1KFORJK1J0PRINTF“PRINTF“3FXD“,AK,KPRINTF“NN“调试结果5、用SIMPSON公式逐次分半算法计算定积分。要求误差不超过106。10分（所需节点处的函数值按需自行计算）DXT102LN【解】INCLUDEINCLUDEDOUBLEFSIMPFDOUBLEXRETURNLOG1X/1XXDOUBLEFSIMPDOUBLEA,DOUBLEB,DOUBLEEPSINTN,KDOUBLEH,T1,T2,S1,S2,EP,P,XN1HBAT1HFSIMPFAFSIMPFB/20S1T1EPEPS10WHILEEPEPSP00FORK0KINCLUDEINCLUDE/定义声明区/INTNDOUBLEA0,B0,H0,X0,Y0,N0,K10,K20,K30,K40,X00,YO0DOUBLEX11DOUBLEYY11DOUBLEYY11/FX,Y函数/DOUBLEFDOUBLEX,DOUBLEYDOUBLERESULT/输入FX,YRESULT12XY/1POWX,2RETURNRESULT/主函数/VOIDMAIN/输入A,B,H,YOA0B2H01YO0NBA/HN1X0APRINTF“数值解X,Y为N“PRINTF“1F,8FN“,X,YWHILE1XX0HK1FX0,YOK2FX0H/2,YOH/2K1K3FX0H/2,YOH/2K2K4FX0H,YOHK3YYOH/6K12K2K3K4/输出X,YPRINTF“1F,8FN“,X,YIFN10NN1X0XYOYELSEBREAKX00X102X204X306X408X510X612X714X816X918X1020YY00YY1014484138YY2020285825YY3021031166FORN3N20NYYN1YYNH/2455FXN,YYN5