solve underdetermined solution choosing solution as closest to guess in matlab

You can use the lsqnonneg function in MATLAB to solve an undetermined system where you want to choose the solution that is closest to a given initial guess. The lsqnonneg function performs non-negative constrained least squares with linear equality constraints.

Here is an example of how you can use lsqnonneg in MATLAB to solve an underdetermined system and choose the solution closest to an initial guess:

main.m
A = randn(3, 5);  % Underdetermined system: 3 equations, 5 variables
b = [1; 2; 3];    % RHS vector

x_guess = [0; 0; 0; 0; 0];  % Initial guess for the solution

x_solution = lsqnonneg(A, b, [], x_guess);

disp(x_solution);
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In the above code snippet, A is the coefficient matrix, b is the right-hand side vector of the underdetermined system, and x_guess is the initial guess for the solution. lsqnonneg is used to find the solution that minimizes the Euclidean norm subject to non-negativity constraints.

You can adjust the size of A, b, and x_guess according to the dimensions of your specific underdetermined system.