Metodos Numericos U de C

Polinomio de Lagrange

x P(x)1.0 0.7651977 1.5 0.51182001.3 0.62008601.6 0.45540221.9 0.28181862.2 0.1103623

xi yi

Lagrange

Polinomio de Newton

x P(x)1.0 0.7651977 1.5 0.51182001.3 0.62008601.6 0.45540221.9 0.28181862.2 0.1103623

xi yi

Newton D

Polinomio de Hermite

x P(x)1.3 0.620086 -0.5220232 1.5 0.51182771.6 0.4554022 -0.5698959 z f(z) Diferencias divididas ==>1.9 0.2818186 -0.5811571 1.3 0.620086

1.3 0.620086 -0.52202321.6 0.4554022 -0.548946 -0.089742671.6 0.4554022 -0.5698959 -0.069833 0.066365561.9 0.2818186 -0.578612 -0.02905367 0.067965561.9 0.2818186 -0.5811571 -0.00848367 0.06856667

xi yi y'i

Hermite

0.002666670.00100185 -0.00277469

Polinomio de Spline

Curva 1 0.3 0 4.1 0.74858156 0 -0.910165481 3 1 -1.63829787 4.3 0.50283688 -0.81914894 0.116312062 3.7 1 -0.94042553 4.1 -0.78652482 -0.47021277 0.156737595 3.96 4.27 5.78 6.6

10 7.113 6.717 4.5

Curva 217 4.520 723 6.124 5.625 5.827 5.2

27.7 4.1curva 3

27.7 4.128 4.329 4.130 3

Si(x)=ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3

xi yi D hi Si(x) ai=f(xi) bi ci di

0 5 10 15 20 25 30 350

2

4

6

8

Spline Cubica

X Y UNION DE VALORES1 4.1 1 3

1.015 4.11122565 1.2 3.156455251.03 4.12243287 1.4 3.30879669

1.045 4.13360323 1.6 3.45291051.06 4.1447183 1.8 3.58468287

1.075 4.15575964 2 3.71.09 4.16670883 2.6 3.93201988

1.105 4.17754743 3.2 4.023474021.12 4.18825702 3.8 4.01891821

1.135 4.19881916 4.4 3.962908271.15 4.20921543 5 3.9

1.165 4.21942738 5.2 3.88759191.18 4.2294366 5.4 3.89537791

1.195 4.23922464 5.6 3.939367971.21 4.24877309 5.8 4.03557202

1.225 4.2580635 6 4.21.24 4.26707745 6.2 4.44141508

1.255 4.2757965 6.4 4.739593321.27 4.28420223 6.6 5.06706403

1.285 4.29227621 6.8 5.396356492 4.3 7 5.7

2.05 4.32310851 7.2 5.956347782.1 4.34220851 7.4 6.16704879

2.15 4.35738723 7.6 6.33957592.2 4.36873191 7.8 6.48140201

2.25 4.37632979 8 6.62.3 4.38026809 8.4 6.7889834

2.35 4.38063404 8.8 6.924210472.4 4.37751489 9.2 7.01494584

2.45 4.37099787 9.6 7.070454142.5 4.36117021 10 7.1

2.55 4.34811915 10.6 7.110072082.6 4.33193191 11.2 7.0788411

2.65 4.31269574 11.8 7.002574082.7 4.29049787 12.4 6.87753804

2.75 4.26542553 13 6.72.8 4.23756596 13.8 6.37996797

2.85 4.20700638 14.6 5.979957292.9 4.17383404 15.4 5.51996263

0 5 10 15 20 25 30 350

2

4

6

8

Valores para Graficar

2.95 4.13813617 16.2 5.019978645 4.1 17 4.5

5.05 4.05951782 17.6 5.1569035.1 4.01680213 18.2 5.77458025

5.15 3.97197048 18.8 6.3138065.2 3.92514043 19.4 6.7353545

5.25 3.87642952 20 75.3 3.82595532 20.6 7.0805425

5.35 3.77383537 21.2 6.997884995.4 3.72018723 21.8 6.78495624

5.45 3.66512846 22.4 6.474684995.5 3.6087766 23 6.1

5.55 3.5512492 23.2 5.967907675.6 3.49266383 23.4 5.84208926

5.65 3.43313803 23.6 5.732317015.7 3.37278936 23.8 5.64836317

5.75 3.31173537 24 5.65.8 3.25009362 24.2 5.59352716

5.85 3.18798165 24.4 5.621353985.9 3.12551702 24.6 5.67241722

5.95 3.06281729 24.8 5.735653646 5.6 25 5.8

6.05 5.59456117 25.4 5.896804776.1 5.59178467 25.8 5.91950173

6.15 5.59149761 26.2 5.83379636.2 5.59352716 26.6 5.60539391

6.25 5.59770042 27 5.26.3 5.60384456 27.14 5.01105906

6.35 5.6117867 27.28 4.801412086.4 5.62135398 27.42 4.57623557

6.45 5.63237353 27.56 4.340706046.5 5.6446725 27.7 4.1

6.55 5.65807802 27.76 4.14471836.6 5.67241722 27.82 4.18825702

6.65 5.68751725 27.88 4.22943666.7 5.70320524 27.94 4.26707745

6.75 5.71930832 28 4.36.8 5.73565364 28.2 4.36873191

6.85 5.75206833 28.4 4.377514896.9 5.76837953 28.6 4.33193191

6.95 5.78441438 28.8 4.237565967 5.8 29 4.1

7.1 5.82927332 29.2 3.925140437.2 5.85552245 29.4 3.720187237.3 5.87821155 29.6 3.49266383

7.4 5.89680477 29.8 3.250093627.5 5.910766257.6 5.919560137.7 5.922650587.8 5.919501737.9 5.90957772

8 5.892342728.1 5.867260868.2 5.83379638.3 5.791413178.4 5.739575648.5 5.677747838.6 5.605393918.7 5.521978028.8 5.426964318.9 5.31981692

8 5.28.035 5.15498905

8.07 5.108441328.105 5.06043769

8.14 5.011059068.175 4.9603863

8.21 4.908500298.245 4.85548192

8.28 4.801412088.315 4.74637163

8.35 4.690441488.385 4.6337025

8.42 4.576235578.455 4.51812157

8.49 4.45944148.525 4.40027593

8.56 4.340706048.595 4.28081262

8.63 4.220676558.665 4.16037872

10 7.110.15 7.10618603

10.3 7.1099656110.45 7.1112804

10.6 7.1100720810.75 7.10628231

10.9 7.0998527811.05 7.09072515

11.2 7.0788411

11.35 7.0641422911.5 7.0465704

11.65 7.0260671111.8 7.00257408

11.95 6.9760329812.1 6.9463855

12.25 6.9135732912.4 6.87753804

12.55 6.8382214112.7 6.79556508

12.85 6.7495107213 6.7

13.2 6.6285834513.4 6.5512309813.6 6.4682550113.8 6.37996797

14 6.2866822514.2 6.1887102914.4 6.086364514.6 5.9799572914.8 5.86980108

15 5.7562082915.2 5.6394913315.4 5.5199626315.6 5.3979345915.8 5.27371963

16 5.1476301816.2 5.0199786416.4 4.8910774416.6 4.7612389916.8 4.6307757