How can I solve system of 6 equations in series?

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Shreen El-Sapa
Shreen El-Sapa 2025-4-22
编辑： Torsten 2025-4-26
How can I solve system of 6 equations in series?
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Sam Chak
Sam Chak 2025-4-22
Ran in:
Attempt to sharpen blurry equations.
a = imread('ss.png');
b = imsharpen(a, Radius=2, Amount=1);
imshow(b)
title('Sharpened Image');
Walter Roberson
Walter Roberson 2025-4-22
Much of the time, equations involving infinite sums are not solvable through any automated system.

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Torsten
Torsten 2025-4-22
移动：Torsten 2025-4-22
There is no summation over i in (5.10) and (5.11) although C_n^i and D_n^i are present. Is this a mistake ?
If you want to stop summation at n = 2, you have a linear system of equation in the 6 unknowns. Write your system as M*[A_2, B_2, C1_2, C2_2, D1_2,D2_2] = rhs with a 6x6 matrix "M" and a 6x1 vector "rhs" and solve for [A_2, B_2, C1_2, C2_2, D1_2,D2_2] by using sol = M\rhs .
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Shreen El-Sapa
Shreen El-Sapa 2025-4-25
function solveSixEquations
% Initial guesses for the variables
initial_guess = ones(6,1); % Assume initial guesses as 1 for all variables
% Call fsolve to solve the system of equations
options = optimoptions('fsolve', 'Display', 'iter');
[solution, fval, exitflag] = fsolve(@equations, initial_guess, options);
% Display the solution
disp('Solution:');
disp(solution);
end
function F = equations(vars)
% Define variables
x1 = vars(1);
x2 = vars(2);
x3 = vars(3);
x4 = vars(4);
x5 = vars(5);
x6 = vars(6);
% Define the system of equations
F(1) = equation1(x1, x2, x3, x4, x5, x6);
F(2) = equation2(x1, x2, x3, x4, x5, x6);
F(3) = equation3(x1, x2, x3, x4, x5, x6);
F(4) = equation4(x1, x2, x3, x4, x5, x6);
F(5) = equation5(x1, x2, x3, x4, x5, x6);
F(6) = equation6(x1, x2, x3, x4, x5, x6);
end
function res = equation1(x1, x2, x3, x4, x5, x6)
% Define your first equation here
res = x1 + x2 - x3; % Example equation
end
function res = equation2(x1, x2, x3, x4, x5, x6)
% Define your second equation here
res = x2 * x4 - x5; % Example equation
end
function res = equation3(x1, x2, x3, x4, x5, x6)
% Define your third equation here
res = x3^2 + x4 - x1; % Example equation
end
function res = equation4(x1, x2, x3, x4, x5, x6)
% Define your fourth equation here
res = x1*x5 + x2*x6 - 1; % Example equation
end
function res = equation5(x1, x2, x3, x4, x5, x6)
% Define your fifth equation here
res = x4^2 + x5*x6 - 2; % Example equation
end
function res = equation6(x1, x2, x3, x4, x5, x6)
% Define your sixth equation here
res = x1 + x2 + x3 + x4 + x5 + x6 - 10; % Example equation
end
Torsten
Torsten 2025-4-26
编辑：Torsten 2025-4-26
Is there a question left or is this just the way you want to solve the original problem ?

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