How do I write this algorithm, I dont understand it and I am stuck.

Ax = b and S is a surrogate smoother

[dpb]

Has to be more context; S, A and b are undefined above...they must come from supporting text prior to the above...

Answer 1

[Gokul Nath S J]

Hi Nathan,

Based on your query, it seems that you would like to implement the algorithm. I can share the general workflow considering some contraints.

The following variables are assumed to be predefined. ()

Considering this constraints,

Step 1: Initialize the variables .

Step 2: Start the for loop from the starting value of k = 1

Step 3: Inside the loop update the value of for the iteration to continue in the next round.

Step 4: Once the loop termination condition occur, update the final value to x and return it.

A reduced code is attached below considering the constraints mentioned in the step 1.

function xk = ChebyshevSmoother(lambda_max, lambda_min, S, A, x, b, chebyshevOrder)
    theta = 0.5*(lambda_max+lambda_min);
    delta = 0.5*(lambda_max-lambda_min);
    sigma = theta/delta;
    rho   = 1/sigma;
    r = S*(b-A*x);
    dk = r/theta;
    xk = 0;
    for k = 1:chebyshevOrder
        xk = xk + dk;
        r = r - S*A*dk;
        rho_kplusone = 1/(2*sigma-rho);
        dk = rho_kplusone*rho*dk + 2*rho_kplusone*r/delta+1;
        rho = rho_kplusone;
    end
    xk = xk +dk;
end

Thanks,

Gokul Nath S J