Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree 2 that fits the data points given in the table above. Approximate f(0.3) using Q(0.3).
Use P(x) = Ax2+Bx +C to find 3 equations and then find A,B,C.
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Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of...
Consider the following table of data points: Using least squares fitting, find the polynomial Q(x) of degree 2 that fit...
Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree
2 that fits the data points given in the table above. Approximate
f(0.3) using Q(0.3).
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663...
Faculty of Engineering A standard full time year of study is equivalent to 8 credit points...
Faculty of Engineering A standard full time year of study is equivalent to 8 credit points or one Equivalent Full-Time Student Load (EFTSL). Course fee rates for a student commencing in 2020 Credit points EFTSL Course fee 0.125 $4,737.50 0.250 $9,475.00 0.375 $14,212.50 0.500 $18,950.00 0.625 $23,687.50 0.750 $28,425.00 0.875 $33,162.50 1.000 $37,900.00 Write some code to do the following: 1. Write a function calcE3001Fees that takes one parameter, creditPoints. This function should calculate the fees due given the creditPoints...
Given the data points (xi , yi), with xi 0 1.2 2.3 3.5 4 yi 3.5 1.3 -0.7 0.5 2.7 find and plot (using MATLAB) the least-squares basis functions and the resulting least-squares fitting functions toget...
Given the data points (xi , yi), with
xi 0 1.2 2.3 3.5 4
yi 3.5 1.3 -0.7 0.5 2.7
find and plot (using MATLAB) the least-squares basis functions
and the resulting least-squares fitting functions together with the
given data points for the case of
a) a linear monomial basis p(x)= {1 x}T .
b) a quadratic monomial basis p(x)= {1 x
x2}T .
c) a trigonometric basis p(x)= {1 cosx sinx}T
Moreover, determine the coefficients a by the Moore-Penrose...
2. Variational method (15 pts each, 30 points total) Fitting of a collection of the data points to a given functional form can be done using variational method. Say, the measured data points are...
2. Variational method (15 pts each, 30 points total) Fitting of a collection of the data points to a given functional form can be done using variational method. Say, the measured data points are given in the table: 1 0 1 Assuming the fitting function is f(x; α, β, ), where α, β, are the variation parameters, the fitting error functional can be formulated as: F[f-E:(f(xi; α., )-%)2. This function is a mere function of the variational parameters, so the...
please write down detailed solution (do not copy 3. [Polynomial interpolation versus least squares fitting, 10pts]...
please write down detailed solution (do not copy
3. [Polynomial interpolation versus least squares fitting, 10pts] Recall how Q7 in HW3 required you to find the cubic best fit to six given data points. This led to a least squares optimization problem. We are given the same points as in HW3: i 01 | 2 | 3 | 4 | 5 X 0.0 0.5 1.0 1.5 2.0 2.5 Y 0.0 0.20 0.27 0.30 0.32 0.33 (a) Write down the least...
Problem 6: Interpolation, least squares, and finite difference Consider the following data table: 2 = 0...
Problem 6: Interpolation, least squares, and finite difference Consider the following data table: 2 = 0 0.2 0.4 0.6 f(x) = 2 2.018 2.104 2.306 A cubic spline interpolation over these data is constructed as a cubic polynomial interpolating over all 4 data points. None of the above. is constructed by piece-wise locally cubic polynomial interpolation that maintains continuity of the first and second derivatives at the data points is constructed by plece-wise locally cubic polynomial interpolation that has discontinuous...
Find the line y = a + bx which best fits the data points (x, y):...
Find the line y = a + bx which best fits the data points (x, y): (0, 1), (1, 1), (1, 2) in the least squares sense. must use matrix
Problem 2: Interpolation, least squares, and finite difference Consider the following data table: 0 2 0.2...
Problem 2: Interpolation, least squares, and finite difference Consider the following data table: 0 2 0.2 2.018 ti f(x) = 0.4 2.104 0.6 2.306 Using Lagrange linear interpolation between data points 22 = 0.2 and as = 0.4, the value obtained at z = 0.3 is (Chop after 2 decimal places) فو واقع = 2.06 2.09 2.03 None of the above. 2.05
C-Programming please. The task is to create second-degree polynomial calculator for the function, its integral and...
C-Programming please.
The task is to create second-degree polynomial calculator for the function, its integral and its derivative. A second-degree polynomial is described by the equation f(x) = ax +bx+c. Evaluation of the derivative gives the instantaneous slope or rate of change as (where f'(x) is the derivative of f(x)): f"(x)=2x+b The integral of the function f(x) (let us call it F(x)) indicates the area underneath the curve. Between points x; and the area A is A = F(x)-F(x), where,...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would comput...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would compute the parameters β | 1 . Namely, if β is the least squares solution of the system Χβ y, what are the matrix X and the right-hand side vector y? what quantity does such β minimize? (b)...
Consider the following table of data points:
Using least squares fitting, find the polynomial Q(x) of degree
2 that fits the data points given in the table above. Approximate
f(0.3) using Q(0.3).
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663 6 0.750 0.56978 0.875 0.46504 8 1.000 0.36788
f(x) i Xi 0 0.000 1.00000 1 0.125 0.98450 2 0.250 0.93941 0.375 0.86882 4 0.500 0.77880 5 0.625 0.67663...
Faculty of Engineering A standard full time year of study is equivalent to 8 credit points or one Equivalent Full-Time Student Load (EFTSL). Course fee rates for a student commencing in 2020 Credit points EFTSL Course fee 0.125 $4,737.50 0.250 $9,475.00 0.375 $14,212.50 0.500 $18,950.00 0.625 $23,687.50 0.750 $28,425.00 0.875 $33,162.50 1.000 $37,900.00 Write some code to do the following: 1. Write a function calcE3001Fees that takes one parameter, creditPoints. This function should calculate the fees due given the creditPoints...
Given the data points (xi , yi), with
xi 0 1.2 2.3 3.5 4
yi 3.5 1.3 -0.7 0.5 2.7
find and plot (using MATLAB) the least-squares basis functions
and the resulting least-squares fitting functions together with the
given data points for the case of
a) a linear monomial basis p(x)= {1 x}T .
b) a quadratic monomial basis p(x)= {1 x
x2}T .
c) a trigonometric basis p(x)= {1 cosx sinx}T
Moreover, determine the coefficients a by the Moore-Penrose...
2. Variational method (15 pts each, 30 points total) Fitting of a collection of the data points to a given functional form can be done using variational method. Say, the measured data points are given in the table: 1 0 1 Assuming the fitting function is f(x; α, β, ), where α, β, are the variation parameters, the fitting error functional can be formulated as: F[f-E:(f(xi; α., )-%)2. This function is a mere function of the variational parameters, so the...
please write down detailed solution (do not copy
3. [Polynomial interpolation versus least squares fitting, 10pts] Recall how Q7 in HW3 required you to find the cubic best fit to six given data points. This led to a least squares optimization problem. We are given the same points as in HW3: i 01 | 2 | 3 | 4 | 5 X 0.0 0.5 1.0 1.5 2.0 2.5 Y 0.0 0.20 0.27 0.30 0.32 0.33 (a) Write down the least...
Problem 6: Interpolation, least squares, and finite difference Consider the following data table: 2 = 0 0.2 0.4 0.6 f(x) = 2 2.018 2.104 2.306 A cubic spline interpolation over these data is constructed as a cubic polynomial interpolating over all 4 data points. None of the above. is constructed by piece-wise locally cubic polynomial interpolation that maintains continuity of the first and second derivatives at the data points is constructed by plece-wise locally cubic polynomial interpolation that has discontinuous...
Problem 2: Interpolation, least squares, and finite difference Consider the following data table: 0 2 0.2 2.018 ti f(x) = 0.4 2.104 0.6 2.306 Using Lagrange linear interpolation between data points 22 = 0.2 and as = 0.4, the value obtained at z = 0.3 is (Chop after 2 decimal places) فو واقع = 2.06 2.09 2.03 None of the above. 2.05
C-Programming please.
The task is to create second-degree polynomial calculator for the function, its integral and its derivative. A second-degree polynomial is described by the equation f(x) = ax +bx+c. Evaluation of the derivative gives the instantaneous slope or rate of change as (where f'(x) is the derivative of f(x)): f"(x)=2x+b The integral of the function f(x) (let us call it F(x)) indicates the area underneath the curve. Between points x; and the area A is A = F(x)-F(x), where,...
3. (25 pts) Consider the data points: t y 0 1.20 1 1.16 2 2.34 3 6.08 ake a least squares fitting of these data using the model yü)- Be + Be-. Suppose we want to m (a) Explain how you would compute the parameters β | 1 . Namely, if β is the least squares solution of the system Χβ y, what are the matrix X and the right-hand side vector y? what quantity does such β minimize? (b)...
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