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Plan1 Resolução da equação x^3 - 9x + 3 = 0 pelo método do ponto fixo. y= x^3 - 9x + 3 j(x(n)) = (x^3+3)/9 y= x^3 - 9x + 3 j(xn) = 9/x - 3/x^2 critério de parada critério de parada y= x^3 - 9x + 3 n xn x(n+1) = j(x(n)) |x(n) - x(n+1)| |f(xn)| n xn x(n+1) = j(x(n)) x(n) - x(n+1) n xn x(n+1) = j(x(n)) x(n+1) - x(n) 0 1.000000 0.444444 0.5555555556 0.9122085048 0 2.5 3.120000 0.62 0 3 2.8844991406 0.1155008594 1 0.444444 0.343088 0.1013565005 0.0474068407 1 3.12 2.576430 -0.5435700197 1 2.8844991406 2.842237717 0.0422614236 2 0.343088 0.337821 0.0052674267 0.0018316643 2 2.5764299803 3.041262 0.4648318223 2 2.842237717 2.8264558535 0.0157818635 3 0.337821 0.337617 0.0002035183 0.0000696362 3 3.0412618026 2.634948 -0.4063135969 3 2.8264558535 2.8205169266 0.0059389269 4 0.337617 0.337609 0.0000077374 0.0000026458 4 2.6349482058 2.983534 0.348585846 4 2.8205169266 2.8182755389 0.0022413877 5 0.337609 0.337609 0.000000294 0.0000001005 5 2.9835340517 2.679534 -0.3040000091 5 2.8182755389 2.817428698 0.0008468409 6 0.337609 0.337609 0.0000000112 0.0000000038 6 2.6795340427 2.940960 0.2614259269 6 2.817428698 2.817108612 0.0003200859 7 0.337609 0.337609 0.0000000004 0.0000000001 7 2.9409599695 2.713374 -0.227585767 7 2.817108612 2.8169876082 0.0001210039 8 0.337609 0.337609 0 0 8 2.7133742025 2.909428 0.1960533068 8 2.8169876082 2.8169418617 0.0000457465 9 0.337609 0.337609 0 0 9 2.9094275093 2.738982 -0.1704456021 9 2.8169418617 2.8169245665 0.0000172952 10 0.337609 0.337609 0 0 10 2.7389819072 2.886000 0.1470183588 10 2.8169245665 2.8169180277 0.0000065388 11 0.337609 0.337609 0 0 11 2.8860002661 2.758315 -0.127684839 11 2.8169180277 2.8169155555 0.0000024721 12 0.337609 0.337609 0 0 12 2.758315427 2.868555 0.1102396225 12 2.8169155555 2.8169146209 0.0000009346 13 2.8685550495 2.772886 -0.0956686457 13 2.8169146209 2.8169142675 0.0000003534 0.337617 raiz com erro de 10^(-3) 14 2.7728864038 2.855542 0.082656062 14 2.8169142675 2.8169141339 0.0000001336 15 2.8555424658 2.783853 -0.0716890924 15 2.8169141339 2.8169140834 0.0000000505 16 2.7838533735 2.845824 0.061970732 16 2.8169140834 2.8169140643 0.0000000191 17 2.8458241055 2.792099 -0.0537246924 17 2.8169140643 2.8169140571 0.0000000072 18 2.7920994131 2.838559 0.0464598636 18 2.8169140571 2.8169140544 0.0000000027 19 2.8385592767 2.798295 -0.0402644205 19 2.8169140544 2.8169140534 0.000000001 20 2.7982948561 2.833125 0.0348299431 20 2.8169140534 2.816914053 0.0000000004 21 2.8331247992 2.802947 -0.0301778421 21 2.816914053 2.8169140528 0.0000000001 22 2.8029469571 2.829057 0.0261104694 22 2.8169140528 2.8169140528 0.0000000001 23 2.8290574265 2.806439 -0.0226187645 23 2.8169140528 2.8169140527 0 24 2.806438662 2.826012 0.0195734142 24 2.8169140527 2.8169140527 0 25 2.8260120762 2.809059 -0.0169535169 25 2.8169140527 2.8169140527 0 26 2.8090585592 2.823731 0.0146727261 26 2.8169140527 2.8169140527 0 27 2.8237312853 2.811024 -0.0127074456 27 2.8169140527 2.8169140527 0 28 2.8110238397 2.822023 0.010998898 28 2.8169140527 2.8169140527 0 29 2.8220227377 2.812498 -0.0095249407 29 2.8169140527 2.8169140527 0 30 2.812497797 2.820743 0.0082448562 30 2.8169140527 2.8169140527 0 31 2.8207426532 2.813603 -0.0071395434 32 2.8136031098 2.819783 0.006180358 2.817429 raiz com erro de 10^(-3) 33 2.8197834678 2.814432 -0.0053515756 34 2.8144318922 2.819065 0.0046327795 35 2.8190646717 2.815053 -0.0040113927 36 2.8150532791 2.818526 0.0034727036 37 2.8185259827 2.815519 -0.0030068406 38 2.8155191421 2.818122 0.002603109 39 2.8181222512 2.815868 -0.0022538598 40 2.8158683914 2.817820 0.0019512635 41 2.8178196549 2.816130 -0.0016894461 42 2.8161302087 2.817593 0.0014626441 43 2.8175928528 2.816326 -0.0012663756 44 2.8163264773 2.817423 0.0010963792 45 2.8174228565 2.816474 -0.0009492513 2.816474 raiz com erro de 10^(-3) Plan2 Plan3
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