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 LINLSQX.OMS Script File: ```# Description: # Solves the minimum norm of a singular linear least squares problem. # # The objective function for this problem is # f(x) = (x(1) + x(2) - 1)^2 + (x(1) + x(2) - 2)^2 # # The partial of f with respect to x(1) or with respect to x(2) is # (x(1) + x(2) - 1) + (x(1) + x(2) - 2) # # The function f is convex, it is minimized when its partials are zero; i.e., # 2 * x(1) + 2 * x(2) - 3 = 0 # x(2) = 1.5 - x(1) # # linlsq will return the x that minimizes |x|^2 subject to x(2) = 1.5 - x(1) # g(x(1)) = |x|^2 = x(1)^2 + x(2)^2 = x(1)^2 + (1.5 - x(1))^2 # g'(x(1)) = 2 * x(1) + 2 * (1.5 - x(1)) = 0 implies that x(1) = .75 # # # f(x) = | A * x - b |^2 where A and b are defined as # clear A = { [1., 1.], [1., 1.] } b = {1., 2.} eps = 1e-7 x = linlsq(A, b, eps) print "x =", x ``` Output: ```x = { 0.75000 0.75000 } ```