連續(xù)逼近與離散逼近

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1、LegendreP@0,xD1LegendreP@1,xDxLegendreP@2,xD1I-1+3x2M2LegendreP@3,xD1I-3x+5x3M2f@x_D=1?H1+25*x^2L11+25x2Integrate@f@xD*LegendreP@0,xD,8x,-1,15125A=Diag

2、onalMatrix@Table@2?H2*n+1L,8n,0,3,:0,0,,0>,:0,0,0,>>357c=Inverse@AD.bArcTan@5D1:,0,H15-28ArcTan@5DL,0>550b??MatrixForm2ArcTan@5D501H15-28ArcTan@5DL1250A??MatrixForm20002000320005200072連續(xù)逼近與離散逼近.nbP1@x_D=Table@LegendreP@i,xD,8i,0,3

3、1005Plot@8f@xD,P1@xD<,8x,-1,1

4、x@@iDD^j,8i,1,5<,8j,0,3

5、0.`,0.`<,81,0.5`,0.25`,0.125`<,81,1.`,1.`,1.`<<連續(xù)逼近與離散逼近.nb3A1??MatrixForm1-11-11-0.50.25-0.12510.0.0.10.50.250.12511.1.1.Y=Table@f@x@@iDDD,8i,1,526c1=LinearSolve@Transpose@A1D.A1,Transpose@A1D.YD80.573702,0.,-0.60629,0.

6、14626753`*t^20.573702-0.60629t2Plot@8f@xD,P2@xD<,8x,-1,1

7、0.0710496,-0.284199,0.426298,-0.284199,0.0710496