Index

SHEET 3A. Excel functions that compute REAL solutions of w13w25 - 6w1w2 - 17 = 0 and 7w12w2 - 3w1w23 + 5 = 0
  A B C D E F G  
1 vector Z vector F matrix J matrix 1/J vector DZ 1
2 = 1 = A2^3*A3^5 - 6*A2*A3 - 17 = 3*A2^2*A3^5 - 6*A3 = 5*A2^3*A3^4 - 6*A2 = INDEX(MINVERSE(C2:D3),1,1) = INDEX(MINVERSE(C2:D3),1,2) = INDEX(MMULT(E2:F3,B2:B3),1,1) 2
3 = 2 = 7*A2^2*A3 - 3*A2*A3^3 + 5 = 14*A2*A3 - 3*A3^3 = 7*A2^2 - 9*A2*A3^2 = INDEX(MINVERSE(C2:D3),2,1) = INDEX(MINVERSE(C2:D3),2,2) = INDEX(MMULT(E2:F3,B2:B3),2,1) 3
4 vector Z vector F matrix J matrix 1/J vector DZ 4
5 = A2 - G2 = A5^3*A6^5 - 6*A5*A6 - 17 = 3*A5^2*A6^5 - 6*A6 = 5*A5^3*A6^4 - 6*A5 = INDEX(MINVERSE(C5:D6),1,1) = INDEX(MINVERSE(C5:D6),1,2) = INDEX(MMULT(E5:F6,B5:B6),1,1) 5
6 = A3 - G3 = 7*A5^2*A6 - 3*A5*A6^3 + 5 = 14*A5*A6 - 3*A6^3 = 7*A5^2 - 9*A5*A6^2 = INDEX(MINVERSE(C5:D6),2,1) = INDEX(MINVERSE(C5:D6),2,2) = INDEX(MMULT(E5:F6,B5:B6),2,1) 6
7 vector Z vector F matrix J matrix 1/J vector DZ 7
8 = A5 - G5 = A8^3*A9^5 - 6*A8*A9 - 17 = 3*A8^2*A9^5 - 6*A9 = 5*A8^3*A9^4 - 6*A8 = INDEX(MINVERSE(C8:D9),1,1) = INDEX(MINVERSE(C8:D9),1,2) = INDEX(MMULT(E8:F9,B8:B9),1,1) 8
9 = A6 - G6 = 7*A8^2*A9 - 3*A8*A9^3 + 5 = 14*A8*A9 - 3*A9^3 = 7*A8^2 - 9*A8*A9^2 = INDEX(MINVERSE(C8:D9),2,1) = INDEX(MINVERSE(C8:D9),2,2) = INDEX(MMULT(E8:F9,B8:B9),2,1) 9

SHEET 3B. Values returned by functions in SHEET 3A.
  A B C D E F G  
1 vector Z vector F matrix J matrix 1/J vector DZ 1
2 1 3 84 74 0.010615 0.027086 -0.103587 2
3 2 -5 4 -29 0.001464 -0.030747 0.158126 3
4 vector Z vector F matrix J matrix 1/J vector DZ 4
5 1.103587 -0.704233 66.401032 70.723010 0.010674 0.029991 -0.007064 5
6 1.841874 0.015103 9.711685 -25.169943 0.004118 -0.028158 -0.003326 6
7 vector Z vector F matrix J matrix 1/J vector DZ 7
8 1.110651 0.009288 68.086503 72.746264 0.010386 0.029748 9.9035E-05 8
9 1.845200 8.6454E-05 9.843821 -25.398696 0.004025 -0.027843 3.4979E-05 9
10 vector Z vector F matrix J matrix 1/J vector DZ 10
11 1.110552 1.5265E-06 68.065095 72.719598 0.010390 0.029751 1.7402E-08 11
12 1.845165 5.1828E-08 9.841791 -25.395911 0.004026 -0.02787 4.7032E-09 12
13 vector Z vector F matrix J matrix 1/J vector DZ 13
14 1.110552 3.5527E-14 68.065092 72.719593 0.010390 0.029751 3.6913E-16 14
15 1.845165 0 9.841790 -25.395911 0.004026 -0.027847 1.4305E-16 15
  A B C D E F G  

Index

URL http://members.aceweb.com/patrussell/approximations/Sheet_3.htm
Unpublished Work. © Copyright 2001 Pat Russell. Updated April 17, 2009.