Tarea-3 ewfew f we f
23
Interpolación cuadratica x= 1/2((x2^2-x3^2)f1+(x3^2-x1^2)f2+(x1^2-x2^29 f(x)= (x-1)^4 Iteración x1 x2 0 0 0.5 1 0.5 1 2 0.83333333 1 3 0.91935484 1 4 0.95996066 1 5 0.98001371 1
description
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Transcript of Tarea-3 ewfew f we f
Interpolación cuadratica
x= 1/2((x2^2-x3^2)f1+(x3^2-x1^2)f2+(x1^2-x2^29f3)/(x2-x3)f1+x3-x1)f2+(x1-x2)f3)
f(x)= (x-1)^4
Iteración x1 x2 x30 0 0.5 21 0.5 1 22 0.83333333 1 23 0.91935484 1 24 0.95996066 1 25 0.98001371 1 2
1/2((x2^2-x3^2)f1+(x3^2-x1^2)f2+(x1^2-x2^29f3)/(x2-x3)f1+x3-x1)f2+(x1-x2)f3)
x f1(x1)=(x-1)^4 f2(x2)=(x-1)^4 f3(x3)=(x-1)^4 f(x)1 1 0.0625 1 0
0.83333333 0.0625 0 1 0.00077160.91935484 0.0007716049383 0 1 4.22974E-050.95996066 4.229735978E-05 0 1 2.57009E-06 3.97273E-050.98001371 2.570085109E-06 0 1 1.59562E-070.99001093 1.595617643E-07 0 1 9.95637E-09
Interpolación cuadratica
f(x)= x^4-20*x^3+0.1*x
Iteracion x1 x2 x3 X f1 f2 f30 0 0.5 2 0.19664804 0 -2.3875 -143.81 0.19664804 0.5 2 0.93551826 0.41650807 0.0625 12 0.5 0.93551826 2 0.81712477 0.0625 1.72881E-05 13 0.5 0.81712477 2 0.79841415 0.0625 0.00111846 14 0.5 0.79841415 2 0.79699899 0.0625 0.00165135 15 0.5 0.79699899 2 0.7969103 0.0625 0.00169822 16 0.5 0.7969103 2 0.79690483 0.0625 0.00170119 17 0.5 0.79690483 2 0.79690449 0.0625 0.00170137 18 0.5 0.79690449 2 0.79690447 0.0625 0.00170138 19 0.5 0.79690447 2 0.79690447 0.0625 0.00170138 1
f(x)-0.130929171.72881E-050.001118460.001651350.001698220.001701190.001701370.001701380.001701380.00170138
Newton
x^k+1= x^k-f'(x^k)/f''(x^k)
f(X)= x^4-20*x^3+0.1*x f(X)= x^4-20*x^3+0.1*xf'(x)= 4*x^3-60*x^2+0.1 f'(x)= 4*x^3-60*x^2+0.1f''(x)= 12*x^2-120*x f''(x)= 12*x^2-120*xx 0.5 x 0
Iteración f'(x^k) f''(x^k) x^k x^k+1 Iteración f'(x^k)1 -14.4 -57 0.5 0.24736842 1 0.12 0.24736842 -3.51092113 -28.9499169 0.12609273 2 #DIV/0!3 0.12609273 -0.84594344 -14.94033529 0.06947128 3 #DIV/0!4 0.06947128 -0.1882344 -8.278638791 0.04673392 4 #DIV/0!5 0.04673392 -0.03063529 -5.581861851 0.04124556 5 #DIV/0!6 0.04124556 -0.0017911 -4.929052615 0.04088218 6 #DIV/0!7 0.04088218 -7.8573E-06 -4.885805685 0.04088057 7 #DIV/0!
x^4-20*x^3+0.1*x f(X)= x^4-20*x^3+0.1*x4*x^3-60*x^2+0.1 f'(x)= 4*x^3-60*x^2+0.112*x^2-120*x f''(x)= 12*x^2-120*x
x 2
f''(x^k) x^k x^k+1 Iteración f'(x^k) f''(x^k) x^k0 0 #DIV/0! 1 -207.9 -192 2
#DIV/0! #DIV/0! #DIV/0! 2 0.9171875 -47.2877014 -99.9677051#DIV/0! #DIV/0! #DIV/0! 3 0.44415772 -11.3860781 -50.9316136#DIV/0! #DIV/0! #DIV/0! 4 0.22060152 -2.7769595 -25.8882019#DIV/0! #DIV/0! #DIV/0! 5 0.11333414 -0.66485474 -13.4459616#DIV/0! #DIV/0! #DIV/0! 6 0.06388772 -0.14385536 -7.61754642#DIV/0! #DIV/0! #DIV/0! 7 0.04500298 -0.02115152 -5.37605445
x^k+10.9171875
0.444157720.220601520.113334140.063887720.045002980.04106859
Quasinewton
x= x^q-f'(x^q)/((f'(x^q)-f'(x^p))/(x^q-x^p)
x^q x^p1 -1
f'(x)= 4*x^3-60*x^2 -55.9 -63.9
Iteración f'(x^q) f'(x^p) x^q x^p x0 -55.9 -63.9 1 -1 14.9751 -55.9 -22.3250625 1 14.975 24.26742982 -55.9 21830.7596 1 24.2674298 1.059426583 -55.9 -62.4867441 1 1.05942658 0.495661924 -55.9 -14.1537462 1 0.49566192 0.324669985 -55.9 -6.0877411 1 0.32466998 0.242135396 -55.9 -3.36098767 1 0.24213539 0.193653827 -55.9 -2.12105873 1 0.19365382 0.161851278 -55.9 -1.45479072 1 0.16185127 0.139455719 -55.9 -1.05602523 1 0.13945571 0.12288586
10 -55.9 -0.7986333 1 0.12288586 0.1101730611 -55.9 -0.62293704 1 0.11017306 0.1001452812 -55.9 -0.4977272 1 0.10014528 0.092061113 -55.9 -0.40539379 1 0.0920611 0.0854285114 -55.9 -0.335388 1 0.08542851 0.0799081615 -55.9 -0.28107787 1 0.07990816 0.0752583516 -55.9 -0.23812413 1 0.07525835 0.0713022617 -55.9 -0.20359072 1 0.07130226 0.0679075318 -55.9 -0.17543335 1 0.06790753 0.0649730919 -55.9 -0.15219305 1 0.06497309 0.0624204520 -55.9 -0.13280588 1 0.06242045 0.0601876621 -55.9 -0.11648115 1 0.06018766 0.0582252522 -55.9 -0.10262119 1 0.05822525 0.0564931623 -55.9 -0.09076742 1 0.05649316 0.0549586524 -55.9 -0.08056319 1 0.05495865 0.0535946925 -55.9 -0.07172766 1 0.05359469 0.0523787626 -55.9 -0.06403723 1 0.05237876 0.0512919527 -55.9 -0.05731206 1 0.05129195 0.0503182828 -55.9 -0.05140612 1 0.05031828 0.0494441429 -55.9 -0.04619985 1 0.04944414 0.0486578830 -55.9 -0.04159453 1 0.04865788 0.0479494731 -55.9 -0.03750812 1 0.04794947 0.0473102332 -55.9 -0.03387188 1 0.04731023 0.0467326133 -55.9 -0.03062795 1 0.04673261 0.0462100234 -55.9 -0.02772725 1 0.04621002 0.04573669
x^q x^p0 0
f'(x)= 4*x^3-60*x^2 0.1 0.1
Iteración f'(x^q) f'(x^p) x^q x^p0 0.1 0.1 0 01 0.1 #DIV/0! 0 #DIV/0!2 0.1 #DIV/0! 0 #DIV/0!3 0.1 #DIV/0! 0 #DIV/0!4 0.1 #DIV/0! 0 #DIV/0!
x^q x^p2 -2
f'(x)= 4*x^3-60*x^2 -207.9 -271.9
x Iteración f'(x^q) f'(x^p) x^q#DIV/0! 0 -207.9 -271.9 2#DIV/0! 1 -207.9 -5.52031348 2#DIV/0! 2 -207.9 328.179042 2#DIV/0! 3 -207.9 -1611.64174 2#DIV/0! 4 -207.9 -83.6605871 2
5 -207.9 -29.2748364 26 -207.9 -14.7893054 27 -207.9 -8.89830035 28 -207.9 -5.93328104 29 -207.9 -4.23346295 2
10 -207.9 -3.16913414 211 -207.9 -2.45878759 212 -207.9 -1.96118508 213 -207.9 -1.59911832 214 -207.9 -1.32748214 215 -207.9 -1.11849017 216 -207.9 -0.95426583 217 -207.9 -0.8228843 218 -207.9 -0.71614342 219 -207.9 -0.62825125 220 -207.9 -0.55502342 221 -207.9 -0.49337589 222 -207.9 -0.44099509 223 -207.9 -0.39611794 224 -207.9 -0.35738182 225 -207.9 -0.32372013 226 -207.9 -0.29428835 227 -207.9 -0.26841075 228 -207.9 -0.24554146 229 -207.9 -0.22523563 230 -207.9 -0.20712777 231 -207.9 -0.19091537 232 -207.9 -0.17634628 233 -207.9 -0.16320899 234 -207.9 -0.15132497 235 -207.9 -0.14054274 2
36 -207.9 -0.13073303 237 -207.9 -0.12178504 238 -207.9 -0.11360331 239 -207.9 -0.10610524 240 -207.9 -0.0992191 241 -207.9 -0.09288232 242 -207.9 -0.08704012 243 -207.9 -0.08164438 244 -207.9 -0.07665271 245 -207.9 -0.0720276 246 -207.9 -0.06773579 247 -207.9 -0.06374772 248 -207.9 -0.06003699 249 -207.9 -0.05658003 250 -207.9 -0.05335568 251 -207.9 -0.05034493 252 -207.9 -0.04753067 253 -207.9 -0.04489745 254 -207.9 -0.04243129 255 -207.9 -0.04011951 256 -207.9 -0.03795061 257 -207.9 -0.03591412 258 -207.9 -0.03400047 259 -207.9 -0.03220097 260 -207.9 -0.03050762 261 -207.9 -0.02891313 262 -207.9 -0.02741078 263 -207.9 -0.02599441 264 -207.9 -0.02465836 265 -207.9 -0.02339739 266 -207.9 -0.02220667 267 -207.9 -0.02108176 268 -207.9 -0.02001852 269 -207.9 -0.01901314 270 -207.9 -0.01806206 271 -207.9 -0.01716201 272 -207.9 -0.01630991 273 -207.9 -0.01550294 274 -207.9 -0.01473843 275 -207.9 -0.01401392 276 -207.9 -0.0133271 277 -207.9 -0.01267581 278 -207.9 -0.01205806 279 -207.9 -0.01147195 280 -207.9 -0.01091572 2
81 -207.9 -0.01038771 282 -207.9 -0.00988639 283 -207.9 -0.0094103 284 -207.9 -0.00895808 285 -207.9 -0.00852843 286 -207.9 -0.00812016 287 -207.9 -0.00773213 288 -207.9 -0.00736328 289 -207.9 -0.0070126 290 -207.9 -0.00667914 291 -207.9 -0.006362 292 -207.9 -0.00606036 293 -207.9 -0.0057734 294 -207.9 -0.00550039 295 -207.9 -0.0052406 296 -207.9 -0.00499338 297 -207.9 -0.00475808 298 -207.9 -0.00453412 299 -207.9 -0.00432091 2
100 -207.9 -0.00411792 2101 -207.9 -0.00392465 2102 -207.9 -0.00374062 2103 -207.9 -0.00356536 2104 -207.9 -0.00339845 2105 -207.9 -0.00323947 2106 -207.9 -0.00308804 2107 -207.9 -0.00294379 2108 -207.9 -0.00280638 2109 -207.9 -0.00267546 2110 -207.9 -0.00255072 2111 -207.9 -0.00243187 2112 -207.9 -0.00231862 2113 -207.9 -0.00221069 2114 -207.9 -0.00210785 2115 -207.9 -0.00200984 2116 -207.9 -0.00191642 2117 -207.9 -0.00182739 2118 -207.9 -0.00174253 2119 -207.9 -0.00166164 2120 -207.9 -0.00158454 2121 -207.9 -0.00151104 2122 -207.9 -0.00144097 2123 -207.9 -0.00137417 2124 -207.9 -0.0013105 2125 -207.9 -0.00124979 2
126 -207.9 -0.0011919 2127 -207.9 -0.00113672 2128 -207.9 -0.0010841 2129 -207.9 -0.00103393 2130 -207.9 -0.0009861 2131 -207.9 -0.00094049 2132 -207.9 -0.00089699 2133 -207.9 -0.00085552 2134 -207.9 -0.00081597 2135 -207.9 -0.00077826 2136 -207.9 -0.0007423 2137 -207.9 -0.000708 2138 -207.9 -0.0006753 2139 -207.9 -0.00064411 2140 -207.9 -0.00061436 2141 -207.9 -0.00058599 2142 -207.9 -0.00055894 2143 -207.9 -0.00053314 2144 -207.9 -0.00050853 2145 -207.9 -0.00048506 2146 -207.9 -0.00046268 2147 -207.9 -0.00044133 2148 -207.9 -0.00042097 2149 -207.9 -0.00040155 2150 -207.9 -0.00038303 2151 -207.9 -0.00036536 2152 -207.9 -0.00034851 2153 -207.9 -0.00033244 2154 -207.9 -0.00031711 2155 -207.9 -0.00030249 2156 -207.9 -0.00028854 2157 -207.9 -0.00027524 2158 -207.9 -0.00026255 2159 -207.9 -0.00025045 2160 -207.9 -0.0002389 2161 -207.9 -0.00022789 2162 -207.9 -0.00021739 2163 -207.9 -0.00020737 2164 -207.9 -0.00019781 2165 -207.9 -0.0001887 2166 -207.9 -0.00018 2167 -207.9 -0.00017171 2168 -207.9 -0.0001638 2169 -207.9 -0.00015625 2170 -207.9 -0.00014905 2
x^p x-2 14.99375
14.99375 15.348180715.3481807 7.1766373
7.1766373 1.233318451.23331845 0.717048870.71704887 0.506786310.50678631 0.392429140.39242914 0.3205471
0.3205471 0.271208940.27120894 0.235273860.23527386 0.207956760.20795676 0.186509
0.186509 0.169238860.16923886 0.155047920.15504792 0.143191840.14319184 0.133148280.13314828 0.124539880.12453988 0.117087160.11708716 0.110578760.11057876 0.104851830.10485183 0.099778870.09977887 0.095258650.09525865 0.091209750.09120975 0.087565930.08756593 0.084272780.08427278 0.081285160.08128516 0.078565320.07856532 0.076081430.07608143 0.073806490.07380649 0.071717410.07171741 0.069794380.06979438 0.068020230.06802023 0.066380090.06638009 0.064860930.06486093 0.063451370.06345137 0.06214136
0.06214136 0.060922010.06092201 0.059785460.05978546 0.058724680.05872468 0.057733420.05773342 0.056806040.05680604 0.0559375
0.0559375 0.055123250.05512325 0.054359180.05435918 0.053641560.05364156 0.052967
0.052967 0.052332430.05233243 0.051735040.05173504 0.051172260.05117226 0.050641740.05064174 0.050141330.05014133 0.049669040.04966904 0.049223050.04922305 0.048801670.04880167 0.048403360.04840336 0.048026680.04802668 0.0476703
0.0476703 0.047332980.04733298 0.047013580.04701358 0.046711040.04671104 0.046424370.04642437 0.046152650.04615265 0.045895010.04589501 0.045650650.04565065 0.045418820.04541882 0.045198820.04519882 0.04499
0.04499 0.044791740.04479174 0.044603450.04460345 0.044424610.04442461 0.0442547
0.0442547 0.044093240.04409324 0.043939780.04393978 0.043793910.04379391 0.043655220.04365522 0.043523340.04352334 0.043397920.04339792 0.043278610.04327861 0.043165120.04316512 0.043057140.04305714 0.04295438
0.04295438 0.042856590.04285659 0.042763520.04276352 0.042674920.04267492 0.042590580.04259058 0.042510280.04251028 0.042433820.04243382 0.042361020.04236102 0.042291680.04229168 0.042225640.04222564 0.042162740.04216274 0.042102830.04210283 0.042045750.04204575 0.041991380.04199138 0.041939580.04193958 0.041890220.04189022 0.041843190.04184319 0.041798370.04179837 0.041755660.04175566 0.041714960.04171496 0.041676170.04167617 0.0416392
0.0416392 0.041603970.04160397 0.041570380.04157038 0.041538370.04153837 0.041507850.04150785 0.041478760.04147876 0.041451030.04145103 0.041424590.04142459 0.041399380.04139938 0.041375350.04137535 0.041352440.04135244 0.0413306
0.0413306 0.041309770.04130977 0.041289910.04128991 0.041270980.04127098 0.041252920.04125292 0.0412357
0.0412357 0.041219290.04121929 0.041203630.04120363 0.0411887
0.0411887 0.041174460.04117446 0.041160890.04116089 0.041147940.04114794 0.041135590.04113559 0.04112382
0.04112382 0.041112590.04111259 0.041101870.04110187 0.041091660.04109166 0.041081920.04108192 0.041072630.04107263 0.041063760.04106376 0.041055310.04105531 0.041047250.04104725 0.041039560.04103956 0.041032230.04103223 0.041025240.04102524 0.041018560.04101856 0.0410122
0.0410122 0.041006130.04100613 0.041000340.04100034 0.040994820.04099482 0.040989550.04098955 0.040984530.04098453 0.040979740.04097974 0.040975170.04097517 0.040970810.04097081 0.040966650.04096665 0.040962680.04096268 0.0409589
0.0409589 0.040955290.04095529 0.040951850.04095185 0.040948560.04094856 0.040945430.04094543 0.040942440.04094244 0.040939590.04093959 0.040936870.04093687 0.040934280.04093428 0.0409318
0.0409318 0.040929440.04092944 0.040927190.04092719 0.040925050.04092505 0.040923
0.040923 0.040921040.04092104 0.040919180.04091918 0.0409174
0.0409174 0.040915710.04091571 0.040914090.04091409 0.040912540.04091254 0.040911070.04091107 0.04090967
Diferencias Finitas
x^k+1= x^k-((f(x+h)-f(x-h))/2h)/(((f(x+h)-2f(x)+f(x-h))/h^2)
f(x)= x^4-20*x^3+0.1*x x= 2
Iteración h= x^k f(x+h) f(x-h) f(x)=x^4-20* f(x+h)=x^4-2 f(x-h)=x^4-20 0.001 2 2.001 1.999 -143.8 -144.007996 -143.5921961 0.001 0.91718743 0.91818743 0.91618743 -14.6319711 -14.6793088 -14.58473342 0.001 0.44415751 0.44515751 0.44315751 -1.66909792 -1.68050947 -1.65773733 0.001 0.22060105 0.22160105 0.21960105 -0.19028186 -0.19307177 -0.187517844 0.001 0.11333317 0.11433317 0.11233317 -0.01761566 -0.01828724 -0.016957525 0.001 0.06388584 0.06488584 0.06288584 0.00119037 0.0010427 0.001330426 0.001 0.04499983 0.04599983 0.04399983 0.0026816 0.00265776 0.002700077 0.001 0.04106462 0.04206462 0.04006462 0.00272436 0.00272098 0.002722838 0.001 0.04087694 0.04187694 0.03987694 0.00272444 0.002722 0.0027229 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.002722
10 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.00272211 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.00272212 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.00272213 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.00272214 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.00272215 0.001 0.04087651 0.04187651 0.03987651 0.00272444 0.002722 0.002722
x= 0
x^k+1 Iteración h= x^k f(x+h) f(x-h) f(x)=x^4-20*0.91718743 0 0.001 0 0.001 -0.001 00.44415751 1 0.001 -49990 -49989.9989 -49990.0009 6.2475E+180.22060105 2 0.001 -32556.6155 -32556.6145 -32556.6165 1.1241E+180.11333317 3 0.001 -21434.2775 -21434.2765 -21434.2785 2.1127E+170.06388584 4 0.001 -14272.6466 -14272.6456 -14272.6476 4.1555E+160.04499983 5 0.001 -9532.39543 -9532.39443 -9532.39643 8.2741E+150.04106462 6 0.001 -6354.59688 -6354.59588 -6354.59788 1.6357E+150.04087694 7 0.001 -4235.46144 -4235.46044 -4235.46244 3.2333E+140.04087651 8 0.001 -2821.7957 -2821.7947 -2821.7967 6.3851E+130.04087651 9 0.001 -1879.62921 -1879.62821 -1879.63021 1.2615E+130.04087651 10 0.001 -1251.44922 -1251.44822 -1251.45022 2.4919E+120.04087651 11 0.001 -832.628237 -832.627237 -832.629237 4.9217E+110.04087651 12 0.001 -552.02122 -552.02022 -552.02222 9.6223E+100.04087651 13 0.001 -366.376624 -366.375624 -366.377624 1.9002E+100.04087651 14 0.001 -242.628401 -242.627401 -242.629401 37511687050.04087651 15 0.001 -160.151639 -160.150639 -160.152639 740001114
x= 0.5
f(x+h)=x^4-2 f(x-h)=x^4-2 x^k+1 Iteración h= x^k f(x+h)9.998E-05 -9.998E-05 -49990 0 0.001 0.5 0.501
6.2475E+18 6.2475E+18 -32556.6155 1 0.001 0.2473681 0.24836811.1241E+18 1.1241E+18 -21434.2775 2 0.001 0.12609191 0.127091912.1127E+17 2.1127E+17 -14272.6466 3 0.001 0.06946961 0.070469614.1555E+16 4.1555E+16 -9532.39543 4 0.001 0.04673099 0.047730998.2741E+15 8.2741E+15 -6354.59688 5 0.001 0.04124166 0.042241661.6357E+15 1.6358E+15 -4235.46144 6 0.001 0.04087812 0.041878123.2333E+14 3.2333E+14 -2821.7957 7 0.001 0.04087651 0.041876516.3851E+13 6.3851E+13 -1879.62921 8 0.001 0.04087651 0.041876511.2615E+13 1.2615E+13 -1251.44922 9 0.001 0.04087651 0.041876512.4919E+12 2.492E+12 -832.628237 10 0.001 0.04087651 0.041876514.9217E+11 4.9217E+11 -553.439821 11 0.001 0.04087651 0.041876519.6222E+10 9.6224E+10 -366.376624 12 0.001 0.04087651 0.041876511.9002E+10 1.9002E+10 -242.628401 13 0.001 0.04087651 0.04187651
3751108041 3751229370 -160.151639 14 0.001 0.04087651 0.04187651739983144 740019083 -105.19902 15 0.001 0.04087651 0.04187651
f(x-h) f(x)=x^4-20* f(x+h)=x^4-2 f(x-h)=x^4-2 x^k+10.499 -2.3875 -2.40192852 -2.37312848 0.2473681
0.2463681 -0.27425276 -0.27777816 -0.2707563 0.126091910.12509191 -0.02723316 -0.02808658 -0.02639468 0.069469610.06846961 0.00026501 7.26289E-05 0.00044911 0.046730990.04573099 0.00263686 0.00260343 0.00266471 0.041241660.04024166 0.00272412 0.00271987 0.00272345 0.040878120.03987812 0.00272444 0.00272199 0.00272201 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.040876510.03987651 0.00272444 0.002722 0.002722 0.04087651
