Group ANSYS

Group Description
Underdetermined systems needing well-conditioned bases to be found.

The goal is to find a permutation or factorization that places A in upper
trapezoidal form, [R1 R2] where R1 is well-conditioned, square, and upper
triangular, and where R1\R2 is as sparse as possible.  Submitted to the
UF collection by Emmannuel Delor, ANSYS.

    opts.tol = 0.01 ;
    [m n] = size(A) ;
    x = ones (n,1) ;
    y = A*x ;
    [c R P info] = spqr (A, y, opts) ;
    info
    Rs = R (:, 1:m) ;    % must be well conditioned
    fprintf ('condest(Rs) %g\n', condest (Rs)) ;
    xs = x (1:m) ;
    xm = x (m+1:n) ;
    A2 = -Rs \ R (:, m+1:n) ;
    y2 =  Rs \ c ;
    norm(A2*xm + y2 - xs)   % should be very small
    nnz (A2)                % should also be as small as possible
Displaying all 3 collection matrices
Id Name Group Rows Cols Nonzeros Kind Date Download File
2652 Delor295K ANSYS 295,734 1,823,928 2,401,323 Least Squares Problem 2011 MATLAB Rutherford Boeing Matrix Market
2651 Delor64K ANSYS 64,719 1,785,345 652,140 Least Squares Problem 2011 MATLAB Rutherford Boeing Matrix Market
2653 Delor338K ANSYS 343,236 887,058 4,211,599 Least Squares Problem 2011 MATLAB Rutherford Boeing Matrix Market