Numerical Methods Library for OCTAVE
Numerical Methods Library for OCTAVE
Numerical Methods Library for OCTAVE
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3.2.1 Normal equation[X, RES] = NORMALEQ(A,B) computes the solution of linear least squares problemmin(norm(A*X-B,2)) solving associated normal equation A’*A*X = A’*B.ParametersA a matrix.B right hand side vector.ReturnsX computed solution.RES value of norm(A*X-B) with X solution computed.3.2.2 Householder[X, RES] = LLS_HQR(A,B) computes the solution of linear least squares problemmin(norm(A*X-B,2)) using Householder QR.ParametersA a matrix.B right hand side vector.ReturnsX computed solution.RES value of norm(A*X-B) with X solution computed.3.2.3 SVD[X, RES] = SVD_LEAST_SQUARES(A,B) computes the solution of linear least squaresproblem min(norm(A*X-B,2)) using the singular value decomposition of A.ParametersA a matrix.B right hand side vector.ReturnsX computed solution.RES value of norm(A*X-B) with X solution computed.3.3 Nonlinear equationsWe will now consider methods <strong>for</strong> solving nonlinear equations. Given a nonlinear function f ,we seek a value x <strong>for</strong> whichf (x) = 0. (2)Such a solution value <strong>for</strong> x is called a root of the equation, and a zero of the function f .Though technically they have distinct meanings, these two terms are in<strong>for</strong>mally used more or9