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Would appreciate a MATLAB code ASAP. splinefit.m is described as below: % least-squares piecewise-polynomial fitting t = [ ... -7.62035373e-01 -4.55770775e-01 -6.30044833e-01 -3.96079961e-01 -3.74279696e-01 -9.34471141e-01

image text in transcribed Would appreciate a MATLAB code ASAP. splinefit.m is described as below:

% least-squares piecewise-polynomial fitting

t = [ ... -7.62035373e-01 -4.55770775e-01 -6.30044833e-01 -3.96079961e-01 -3.74279696e-01 -9.34471141e-01 -9.86832008e-01 -1.62530918e-01 -7.40645986e-01 -7.65669039e-01 -4.35516449e-03 -5.29736492e-01 -1.63538549e-01 -5.23646791e-01 -3.60931859e-01 -8.49383576e-01 -3.65139342e-01 -1.31954693e-01 -4.76818790e-01 -2.58748144e-01 -3.28588525e-01 -9.35968562e-01 -2.41769754e-01 -4.08900417e-01 -6.98732340e-01 -9.68988249e-01 -1.34472763e-01 -5.27250911e-01 -2.81176076e-01 -1.21187200e-01 -2.85870516e-01 -7.89013324e-02 -6.05036596e-01 -1.99091229e-01 -5.55378944e-01 -6.44132783e-02 -1.21133340e-01 -9.02545690e-01 -8.64031140e-01 -7.83013059e-01 -3.45198611e-02 -5.63838133e-01 -3.73351709e-01 -6.98973802e-01 -4.92757016e-01 -6.14133741e-01 -6.49089511e-01 -4.14925893e-01 -4.15748207e-01 -9.57982292e-02 6.81982137e-01 9.28945601e-01 8.56400566e-01 9.90989645e-01 6.71273542e-01 1.63099622e-01 8.60637533e-01 9.64632947e-01 9.04695985e-01 5.69107503e-01 7.13817020e-01 2.11124984e-01 8.31607930e-01 5.73532352e-01 2.84957462e-01 6.34605771e-02 8.53942488e-01 9.89806015e-01 8.85180931e-02 8.00595321e-01 4.10461827e-01 1.50765374e-01 2.93891247e-01 7.68791887e-01 8.72767025e-01 4.41900611e-02 6.14532529e-01 4.49402435e-02 7.18440477e-01 3.30954146e-01 8.80905307e-01 9.80635757e-01 5.05420374e-01 9.98508945e-01 3.09670053e-01 7.69707047e-02 5.99762809e-01 3.13777622e-02 1.97384856e-01 4.07936136e-01 6.10467123e-01 1.56198991e-01 4.24358247e-02 8.67779034e-01 3.13830520e-01 9.58659426e-01 8.96659641e-01 3.77789239e-01 4.60409633e-01 5.20072985e-01 ]; y = [... 2.11974376e-01 3.88773507e-01 4.91956564e-01 4.45308388e-01 3.88162343e-01 1.00704960e-01 2.03784618e-02 4.26427442e-01 4.46112108e-01 3.61211632e-01 4.05088525e-01 3.72774476e-01 4.58122545e-01 3.69994855e-01 4.13245540e-01 2.28566642e-01 4.50220959e-01 4.04192489e-01 4.88925596e-01 3.82278983e-01 4.14375913e-01 1.50235745e-01 2.69664697e-01 3.96604418e-01 3.67473199e-01 4.54684535e-02 4.05240372e-01 4.73810000e-01 4.03613145e-01 3.98946520e-01 3.99702280e-01 4.70807875e-01 4.06369247e-01 4.07783536e-01 4.16279356e-01 3.89922796e-01 3.65028713e-01 1.86604631e-01 2.06406549e-01 4.00188335e-01 4.28102909e-01 4.97501585e-01 2.81611113e-01 4.60758291e-01 3.87431466e-01 4.20216084e-01 4.46837060e-01 3.39021718e-01 3.69750951e-01 4.43402091e-01 -3.68317384e-01 -2.05953922e-01 -2.29363861e-01 -7.15742539e-02 -3.77793976e-01 1.73341412e-01 -2.71407148e-01 4.75705118e-03 -2.28845330e-01 -3.69010373e-01 -3.68145320e-01 -6.93462224e-02 -2.15730121e-01 -3.83335046e-01 -2.15483311e-01 3.04866898e-01 -2.58970384e-01 5.63532504e-02 3.06617527e-01 -1.58414881e-01 -2.06854868e-01 7.09107126e-02 -1.47327089e-01 -3.38390818e-01 -1.29882571e-01 3.63910524e-01 -4.43224091e-01 3.09311036e-01 -3.27364184e-01 -1.40265965e-01 -1.90304444e-01 -2.43093102e-02 -3.85759689e-01 4.60203655e-02 -1.82875791e-01 2.66745380e-01 -3.15924453e-01 3.08730059e-01 -6.61666742e-02 -3.04443009e-01 -3.95902069e-01 5.81697769e-02 2.47443900e-01 -1.68572800e-01 -1.73257495e-01 -4.60740368e-02 -2.04506522e-01 -1.94157482e-01 -2.77704024e-01 -2.10530714e-01 ];

10.11 Least squares fit of piecewise-polynomial function. This exercise is on the piecewise-polynomial fitting prob- lem of page 340 of the textbook. Download the file splinefit.m and run it in MATLAB/Octave to create two arrays t and y of length 100. The vector t contains 100 points in the interval [-1,1]. The first 50 points are in (-1,0], the last 50 in [0,1]. You are asked to find two cubic polynomials p(x) = 0, +422 +032? +047", 9(x) = 45 +062 +672 +0gr), that give the best least squares fit on the intervals (-1,0) and (0,1), respectively, and satisfy the continuity constraints p(0) = 90), (0) = ('0): 50 100 i=1 i=51 minimize (Pft.) 9:)? + (4(t.) - 4:)? subject to p(0) = (0), 10) = 20). The variables are the coefficients 61, ..., 65. Formulate this as a constrained least squares problem minimize || Ac - 6|12 subject to Card and compute the solution by solving the optimality conditions AA CT 0 In MATLAB/Octave: sol - [ A'*A, C'; C, zeros(p,p) ] [A'*b; d ]; x = sol(1:n); 10.11 Least squares fit of piecewise-polynomial function. This exercise is on the piecewise-polynomial fitting prob- lem of page 340 of the textbook. Download the file splinefit.m and run it in MATLAB/Octave to create two arrays t and y of length 100. The vector t contains 100 points in the interval [-1,1]. The first 50 points are in (-1,0], the last 50 in [0,1]. You are asked to find two cubic polynomials p(x) = 0, +422 +032? +047", 9(x) = 45 +062 +672 +0gr), that give the best least squares fit on the intervals (-1,0) and (0,1), respectively, and satisfy the continuity constraints p(0) = 90), (0) = ('0): 50 100 i=1 i=51 minimize (Pft.) 9:)? + (4(t.) - 4:)? subject to p(0) = (0), 10) = 20). The variables are the coefficients 61, ..., 65. Formulate this as a constrained least squares problem minimize || Ac - 6|12 subject to Card and compute the solution by solving the optimality conditions AA CT 0 In MATLAB/Octave: sol - [ A'*A, C'; C, zeros(p,p) ] [A'*b; d ]; x = sol(1:n)

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