The code provided for newt3d.m is as follows:

format long e TOL = .000001; %relative error tolerance x = %initial guess; x is "current" iterate xp = x; %store as previous iterate xp %call function to generate right-hand-side, -f %call function to generate matrix, DF [L,U,P] = lu(DF); %Use MATLAB function to do PA=LU factorization %Use our functions in elearning, forsub and backsub, as appropriate %x is the current iterate %s is the difference between current and previous iterate while norm(s)orm(x) >= TOL %store previous iterate xp = x; %generate right-hand-side, -f %generate matrix, DF [L,U,P] = lu(DF); %PA=LU factorization %Use our functions forsub and backsub as appropriate end x %display last iterate and relerr estimate norm(s)orm(x)

MATLAB Problems: 3) A civil engineer can predict how far a large heavy object (such as a pier) will sink into the ground by finding out how far smaller objects will sink. The amount of pressure p in lb/sq.in. required to sink a circular plate of radius r (in.) a distance of 1 ft in soft soil can be approximated by the following equation: where ki,k2, and k, are parameters that depend on the specific type of soil. Find approximations for the values of k,k,, and k, if a plate with radius of 1 in. requires a pressure of 10 lb/sq.in. to sink 1 ft, a plate with radius 2 in. requires a pressure of 12 lb/sq.in. to sink 1 ft, and a plate with radius 3 in. requires a pressure of 15 lb/sq.in. to sink 1 ft To find the parameters, use Multivariate Newton's Method to solve a system of nonlinear equations by adding code to the script newt3d.m per the comments in the script (script provided in eLearning) and providing the functions genmatrix(x) and genrhs(x): genmatrix(x) will accept a 3x1 vector and output a 3x3 matrix, and genrhs(x) will accept a 3x1 vector and output a 3xl vector. Choose an appropriate initial guess Note: before applying the three equations in the MATLAB functions, you may first need to change the form of the equations, viz., isolating the exponential function in each equation and taking the log of both sides. Per our discussion in class about conditioning, why do you think this may be necessary