Creates the augmented matrix of a. This is given by
[c * eye(m, m),a; a', zeros(n, n)]This is related to the leasted squared solution of a
\\
b, bys * [ r / c; x] = [b, zeros(n, columns(b)]where r is the residual error
r = b - a * xAs the matrix s is symmetric indefinite it can be factorized with
lu
, and the minimum norm solution can therefore be found without the need for aqr
factorization. As the residual error will bezeros (
m,
m)
for under determined problems, and example can bem = 11; n = 10; mn = max(m ,n); a = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],[-1,0,1], m, n); x0 = a \ ones (m,1); s = spaugment (a); [L, U, P, Q] = lu (s); x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)]))); x1 = x1(end - n + 1 : end);To find the solution of an overdetermined problem needs an estimate of the residual error r and so it is more complex to formulate a minimum norm solution using the
spaugment
function.In general the left division operator is more stable and faster than using the
spaugment
function.