实验三插值与数值积分

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1、数学实验三插值与数值积分【实验目的】1.掌握用MATLAB计算拉格朗口、分段线性、三次样条三种插值的方法，改变节点的数冃，对三种插值结果进行初步分析；2•寧握用MATLAB及梯形公式、辛普森公式计算数值积分；3.通过实例学习用插值和数值积分解决实际问题。【实验内容】题1(3)选择一些函数，在n个节点上(n不要太大，如5~11)用拉格朗日、分段线性、三次样条三种插值的方法，计算m个插值点的函数值(m要适中，如50-100)0通过数值和图形输出，将三种插值结果与精确值进行比较，适当增加n,再作比较，由此作初步分析。下列函数供选择参考：(3)y二cos"x,・2WxW2解：当n=8,m=50时,在

2、matlab中编程如下:x=-2:0.5:2;y=(cos(x)).A10;a=-2:4/50:2;yy=(cos(a)).A10;yl=lagr(x,y,a);y2=interpl(x“a);y3=interpl(x,y,a/spline,)；[a;yy;yl;y2;y3]'数值输出如下:-20.000155760.000155760.000155760.00015576-1.922.1987e-005-0.992890.000130840.0019267-1.841.771e-006-1.23940.000105920.0027391-1.765.538e-008-1.0788.0997

3、e-0050.0027867-1.682.3645e-010-0.740095.6075e-0050.0022632・1.64.5057e-016-0.373453.1153e-0050.0013621-1.521.1388e-013-0.0632966.2305e-0060.00027724-1.441.4242e-0090.15090.00025442-0.00079778-1.361.6085e-0070.261290.00059364-0.0016693-1.283.7541e-0060.280380.00093287-0.0021436-1.23.9028e-0050.232090

4、.0012721-0.0020271-1.120.000246430.144950.0016113-0.001126-1.040.00110510.0471670.00195050.0007532-0.960.0038502-0.036860.0236260.0039155-0.880.011026-0.0885930.0666380.011223-0.80.026946-0.0964010.109650.028094-0.720.057684-0.0557170.152660.06006-0.640.110220.0314770.195670.11265-0.560.190610.1576

5、60.238690.19139-0.480.301450.31110300110.30176-0.40.439420.47740.416760.44195-0.320.593940.641020.53340.59603-0.240.747660.786850.650050.74643-0.160.879370.901590.76670.8756-0.080.968470.974830.883350.96597011110.080.968470.974830.883350.965970.160.879370.901590.76670.87560.240.747660.786850.650050

6、.746430.320.593940.641020.53340.596030.40.439420.47740.416760.441950.480.301450.31110.300110.301760.560.190610.157660.238690.191390.640.110220.0314770.195670.112650.720.057684-0.0557170.152660.060060.80.026946-0.0964010.109650.0280940.880.011026-0.0885930.0666380.0112230.960.0038502-0.036860.023626

7、0.00391551.040.00110510.0471670.00195050.00075321.120.000246430.144950.0016113-0.0011261.23.9028e-0050.232090.0012721-0.00202711.283.7541e-0060.280380.00093287-0.00214361361.6085e-0070.261290.00059364-0.001