Minimizing an equation to 0

I have an equation where I am trying to reduce the RMS to 0 i.e RMS(A-(B+C)<=0. A,B and C are known but the RMS is not equal to 0 . Now, I want to modify this equation such that RMS(A-(k1*B+k2*C)<=0. I want to find k1 and k2 to make the RMS as close to 0. How could I do this?

[Walter Roberson]

are A, B, C matrices? Are k1 and k2 scalar?

[AAS]

yes, A,B and C are matrices and k1 and k2 are scalars.

Answer 1

[Alan Stevens]

Try fminsearch

[AAS]

I tried to implement it this way.. however, it did not produce good resuts, barely did any minimization. Am I implementing it right?

f = @(k) rms(C-(k(1)*A+k(2)*B));;

k0=[1 1];

[xmin] = fminsearch(f,k0,options);

f(xmin);

Answer 2

[Torsten]

A = [4 3; 6 2; 7 -3];
B = [1 -3; 2 2; 5 -pi];
C = [12 -0.5; 7 -3; 0 1];
fun = @(p)reshape(A-(p(1)*B+p(2)*C),[],1);
sol = lsqnonlin(fun,[1 1])

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

sol = 1×2

0.9421 0.3061

error = rms(fun(sol))

error = 2.7826

Answer 3

[Bruno Luong]

This minimize the frobenius norm, or l2 norm of the vectorized residual matrix (divided by sqrt(numel(A)) you'll get the rms)

k=[B(:),C(:)]\A(:);
k1=k(1);
k2=k(2);