函数插值-习题课

1、课程回顾课程回顾+习题课习题课nnnxxxxfx 0),()(lim 其其它它0,)(101010 xxxxxxxxl njjjxlyx0)()( 其它其它0,)(1101nnnnnxxxxxxxxl 其它其它0,)(111111iiiiiiiiiiixxxxxxxxxxxxxxxl)(max),(max,)()()(xfMxxhMhxxfxRbxaiini 11021其中8211)(xxfy5 , 0ixi 0)5 , 1 , 0(i)5 . 4(f0123451.000000.500000.200000.100000.058820.03846ix211iixy5 , 1 (0 1 , 01

2、)(0 xxxxl 1, 15 , 00 1,) 1(, 11)(iixiixixiixixxli)4 , 005 , 44)(xxxxln)(10000. 0)(20000. 0)(50000. 0)()(3210 xlxlxlxlx)(03846. 0)(05882. 054xlxl)5 . 4(03846. 0)5 . 4(05882. 0)5 . 4()5 . 4(54llf5 . 003846. 05 . 005882. 004864. 004706. 0)5 . 4(f课程回顾课程回顾+习题课习题课1111)( iiiiiiiiMxxxxMxxxxxS)()(6)(6)()(113

3、31iiiiiiiixxDxxCMhxxMhxxxS )()(6)()()()(6)()()(11111331 iiiiiiiiiiiiiiiMxxMxxhhxfxxxfxxhMxxMxxxS)1,.,2 , 1(211 nidMMMiiiiii iiiiiihhh 1;1nnnnnnnnnMdddMdMMMM112201112212122212222)1,.,2 , 1(211 nidMMMiiiiii )()(6)()()()(6)()()(11111331 iiiiiiiiiiiiiiiMxxMxxhhxfxxxfxxhMxxMxxxS)1,.,2 , 1(211 nidMMMiiiii

4、i iiiiiihhh 1;1nnnnnnnnnMdddMdMMMM112201112212122212222iiiiiihhh11;nnnnnnnnnMdddMdMMMM112201112212122212222 6667. 03333. 0,3333. 0,6667. 02211 iiiiiihhh11; 55526667. 06667. 0221MM 05.1790625.3580625.239125.53725.5975.1735625.1415 .37875.321875.831875.72875.21)(232323xxxxxxxxxxS5 . 1 , 4 . 1 4 . 1 ,

5、2 . 1 2 . 1 , 1 . 1 xxx)()(6)()()()(6)()()(11111331 iiiiiiiiiiiiiiiMxxMxxhhxfxxxfxxhMxxMxxxS插值插值 习题习题030045060,2221050sin000050,60,45,30185,3,4,6233,47601. 02343418522343185185185sin1L595006.03sin612931854185)sin(2118521R3,4,67654. 0234363418561852234643185618521364631854185185185sin2L4000767. 06cos99234318541856185)cos(6118532R13若 函 数 53)(47xxxxf, 求 ,710 xxxf和,810 xxxf 1！7！7！72227710)(,)(ff0！80！82228810)(,)(ff解 有！因10,)(,)(nfxxxfnn ( )( )0.400.550.650.800.90()0.410750.578150.696750.88811 1.02652(0.596)kkf xshxxf xNewtonf例已知表如下用插值公式求的近似值。0.410751.1160(0.40) 0.2800(0.40)(0.55) 0.19