(48) Complex Roots Of Multiple Non-Linear Equations (Newton-Raphson Method)
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03-13-2018, 02:47 PM
(This post was last modified: 03-14-2018 10:20 PM by gerry_in_polo.)
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(48) Complex Roots Of Multiple Non-Linear Equations (Newton-Raphson Method)
Complex Roots of Multiple Non-Linear Equations Via Newton-Raphson Method, HP-48
Gerardo V. Lozada, M.S., P.E.E., May 12, 2015 Computes the real and complex roots of a system of simultaneous non-linear equations using the Newton-Raphson Method utilizing the forward difference method to approximate the Jacobian matrix. Input parameters on the stack: MQ - A list containing the simultaneous non-linear equations, each enclosed in single quotes ' ', the number n of variables should equal the number of equations. Variables are denoted as X(1), X(2), X(3) ...... X(n). X0 - Array containing the initial estimate of the roots, may be real or complex. Example: Find the roots of the three simultaneous equations X1^2 - 2*X1*X2 + X2^2 - ln(X3) = 16, X1^2 - X2^2 + 20*sin(X3) = 9 and X1^3 + X2^2 + X3^2 = -27 using initial estimates of X1=1-j7, X2=2+j10 and X3=-4-j11. Enter {'X(1)^2-2*X(1)*X(2)+X(2)^2-LN(X3)-16' 'X(1)^2-X(2)^2+20*SIN(X)-9' 'X(1)^3+X(2)^2+X(1)^2+27'} and [(1,-7) (2,10) (-4,-11)] on the stack and then run the program NR. The resulting complex roots are: X = [(1.1215, 4.0809) (5.313, 3.7512) (-3.9988, -1.588) ] converged in 15 iterations. Final estimate error is 4.5802e-7. Other root combinations may be found depending on the initial root estimates used. Program NR << -> MQ X0 << 1e-6 'TL' STO MQ SIZE 'N' STO X0 'X' STO IF X0 TYPE 4 == THEN (0.01,0.01) 'D' STO ELSE 0.01 'D' STO END 0 'ITER' STO DO 0 'YM' STO 1 N FOR I MQ I GET ->NUM NEXT N ->ARRY 'Y' STO 1 N FOR I Y I GET ABS 'YI' STO IF YI YM > THEN YI 'YM' STO END NEXT IF YM TL >= THEN 1 N FOR I 1 N FOR J X J GET D + X J 3 ROLL PUT 'X' STO MQ I GET ->NUM Y I GET - D / X J GET D - X J 3 ROLL PUT 'X' STO NEXT N ->ARRY NEXT N ROW-> 'JAC' STO Y JAC / 'DX' STO X DX - 'X' STO END ITER 1+ 'ITER' STO UNTIL YM TL < END MQ X "X" ->TAG ITER "ITER" ->TAG YM "YM" ->TAG >> >> |
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(48) Complex Roots Of Multiple Non-Linear Equations (Newton-Raphson Method) - gerry_in_polo - 03-13-2018 02:47 PM
RE: (48) Complex Roots Of Multiple Non-Linear Equations (Newton-Raphson Method) - pier4r - 03-13-2018, 03:01 PM
RE: (48) Complex Roots Of Multiple Non-Linear Equations (Newton-Raphson Method) - acser - 04-18-2023, 02:48 AM
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