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• If you have questions about the grading of the homeworks: Please contact the grader

  Feiyue Li, office MTH 4423, e-mail lify@math.umd.edu, office hours Mon Wed 1:00-2:00pm

• Try out the Java applet for interpolating polynomials and splines
• Assignment 2
  • Problem 1d: Change to ``... choosing the sign in b3tilde such that |y3tilde| becomes as large as possible...''
  • Problem 3: Change to ``... which solves the linear system Ax = b ...''

    You get 16 equations, expressing that the temperature at each of the 16 interior grid points is the arithmetic mean of the four neighboring gridpoints. The equations should look like this

    u₁ = (t₁ + u₂ + u₅ + t₄)/4

    .

    .

    .

    u₁₆ = (u₁₂ + t₂ + t₃ + u₁₅)/4

    You then put all the unknowns u_j on the left hand side and get a linear system Au = b with a certain 16 by 16 matrix A, and a vector b of length 16.

    Use surf(reshape(u,4,4)) where u is the solution vector of length 16. This plots the temperature on the vertical axis over all the interior gridpoints. To plot the temperature over all gridpoints including the boundary you can use the following:

    u1 = zeros(6,6);
    u1(:,1) = t1;
    u1(:,6) = t3;
    u1(1,:) = t4;
    u1(6,:) = t2;
    u1(2:5,2:5) = reshape(u,4,4);
    surf(u1)

  • Problem 2(b), 3: For finding the estimated condition number use the Matlab function rcond(A) which approximates 1/cond₁(A).