NewtonsApproximation.xlsx

# NewtonsApproximation.xlsx - %error Remarks FINAL(Real...

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%error Remarks FINAL (Real root/zero) 2 5 11 0.454545455 1.5454545 29.4117647 AGAIN 1 1.5454545455 1.1457551 6.1652893 0.18583963 1.3596149 13.6685489 AGAIN 1.3596149159 0.1537049 4.5456582 0.033813571 1.3258013 2.55042515 AGAIN 1.325801345 0.0046249 4.2732476 0.001082296 1.324719 0.08170001 AGAIN 1.3247190494 4.66E-006 4.2646417 1.0922E-006 1.324718 8.245E-005 AGAIN 1.3247179572 4.74E-012 4.264633 1.1116E-012 1.324718 8.391E-011 STOP 1.3247179572 y = (x/4) - sin x %error Remarks FINAL (Real root/zero) 3 0.60888 1.2399925 0.491035223 2.5089648 19.5712282 AGAIN 2 2.5089647771 0.0359751 1.0564765 0.034051941 2.4749128 1.37588447 AGAIN 2.4749128357 0.0003481 1.0358791 0.000336015 2.4745768 0.01357867 AGAIN 2.4745768211 3.49E-008 1.0356713 3.3712E-008 2.4745768 1.362E-006 STOP 2.4745767874 y = 2x - 5 - sin x %error Remarks FINAL (Real root/zero) 3 0.85888 2.9899925 0.287251554 2.7127484 10.5889492 AGAIN 3 2.7127484457 0.0096769 2.909447 0.003326042 2.7094224 0.12275834 AGAIN 2.7094224038 2.31E-006 2.9080589 7.9283E-007 2.7094216 2.926E-005 STOP 2.7094216109 %error Remarks FINAL (Real root/zero) 2.000 3.000 9.000 0.333 1.667 20.000 AGAIN 4 1.667 0.630 5.333 0.118 1.549 7.623 AGAIN 1.549 0.068 4.195 0.016 1.532 1.059 AGAIN 1.532 0.001 4.045 0.000 1.532 0.020 AGAIN 1.532 0.000 4.042 0.000 1.532 0.000 STOP 1.532 √(3) %error Remarks FINAL (Real root/zero) 2.00000 1.00000 4.00000 0.25000 1.75000 14.28571 AGAIN 5 1.75000 0.06250 3.50000 0.01786 1.73214 1.03093 AGAIN 1.73214 0.00032 3.46429 0.00009 1.73205 0.00531 AGAIN 1.73205 0.00000 3.46410 0.00000 1.73205 0.00000 STOP 1.73205 Enhancement #1 %error Remarks FINAL (Real root/zero) 4.00 131.00 256.00 0.51 3.49 14.67 AGAIN E#1 A 3.49 23.06 169.78 0.14 3.35 4.05 AGAIN 3.35 1.31 150.71 0.01 3.34 0.26 AGAIN 3.34 0.01 149.54 0.00 3.34 0.00 AGAIN 3.34 0.00 149.53 0.00 3.34 0.00 STOP 3.34 f(x) = x 3 - x - 1 X n f(X n ) f'(X n ) f(X n )/f'(X n ) X n+1 x 1 = x 2 = x 3 = x 4 = x 5 = x 6 = x 7 = X n f(X n ) f'(X n ) f(X n )/f'(X n ) X n+1 x 1 = x 2 = x 3 = x 4 = x 5 = X n f(X n ) f'(X n ) f(X n )/f'(X n ) X n+1 x 1 = x 2 = x 3 = x 4 = y = x 3 - 3x + 1 X n f(X n )

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