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5. Consider the following graph of dats (a) If you wanted to fit a Lagrangian polynomial...
matlab D [10 pts Consider following data points Groups a) Use linear interpolation method to fit...
matlab
D [10 pts Consider following data points Groups a) Use linear interpolation method to fit data. Use 'interp1 b) Fit data with a cubie spline. Use "spline e) Fit a 4h degree polynomial using "polyf Tools Help Make a figure for each of the interpolation methods. In each figure show data points using ocircle marks, a curve that eorresponds to the interpolation method
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit...
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit the given data with a quadratic spline. (b) Find an approximate value of f(3) using the first-degree spline. 6. (20) Consider the table X 0 | 2 | y = f(x) | 7 11 | 3 5 (a) Fit the given data with a quadratic spline. YE (b) Find an approximate value of f (3) using the first-degree spline.
A wind tunnel test conducted on an airfoil section yielded the following data between the lift...
A wind tunnel test conducted on an airfoil section yielded the following data between the lift coefficient (CL) and the angle of attack (?): 12 1.40 16 1.71 20 1.38 de CL 0.11 0.55 0.95 You are required to develop a suitable polynomial relationship between ? and CL and fit a curve to the data points by the least-squares method using (a) hand calculations and (b) Matlab programming Hint: A quadratic equation (parabola) y(x)-aa,x +a x' can be used in...
16. (8 points) Consider the following possible rough sketch of the graph of a polynomial function....
16. (8 points) Consider the following possible rough sketch of the graph of a polynomial function. Which of the following polynomial functions most closely matches the above graph? (a) plz) = (z + 4)(z + 2)(z-1)(z-3) (b) p@) = (z + 4)(z + 2)(3.? + 1) Clearly CIRCLE your answer, and below, use 1-2 sentences to JUSTIFY your answer, citing the specific features of the graph that distinguish your choice from the other choices.
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...
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...
Consider the following points. (-1, 5), (0, 0), (1, 1), (4, 58) (a) Determine the polynomial...
Consider the following points. (-1, 5), (0, 0), (1, 1), (4, 58) (a) Determine the polynomial function of least degree whose graph passes through the given points. p(x) = (b) Sketch the graph of the polynomial function, showing the given points. y 2 3 4 2 3 -10 -20 -20 -30 -40 -40 -60 -50 -601 -80 у BOF у 60 50 60 40 40 30 20 20 10 х 2 3 4 2 3
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 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)d...
help wanted??
thank you
explain correctly
Problem 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)dr(Note: use 0.5 increments forx) b) sina d INote: use a MATLAB function to subdivide the interval into eight equal parts) c e dx (Note: use 0.25 increments for x Problem 2 Use the Simpson's rule to evaluate the following integrals aDdr Problem 3: Given the polynomial: x3-6x2 + 30-0, Use MATLAB to find all roots of this polynomial. Use MATLAB's...
Matlab: a) Write a program to compute the first-degree and third-degree polynomials that fit the data,...
Matlab:
a) Write a program to compute the first-degree and third-degree
polynomials that fit the data, displaying the polynomial
coefficients. Remember to include text to describe the displayed
coefficients.
(b) Compute and display (including what the information is) the
sum of the squares for each curve fit.
(c) Plot the data and the two curve fits on a
single plot, for 101 values of A in the range 0 ?
A ? 9. Choose different line styles for each curve...
matlab
D [10 pts Consider following data points Groups a) Use linear interpolation method to fit data. Use 'interp1 b) Fit data with a cubie spline. Use "spline e) Fit a 4h degree polynomial using "polyf Tools Help Make a figure for each of the interpolation methods. In each figure show data points using ocircle marks, a curve that eorresponds to the interpolation method
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit the given data with a quadratic spline. (b) Find an approximate value of f(3) using the first-degree spline. 6. (20) Consider the table X 0 | 2 | y = f(x) | 7 11 | 3 5 (a) Fit the given data with a quadratic spline. YE (b) Find an approximate value of f (3) using the first-degree spline.
A wind tunnel test conducted on an airfoil section yielded the following data between the lift coefficient (CL) and the angle of attack (?): 12 1.40 16 1.71 20 1.38 de CL 0.11 0.55 0.95 You are required to develop a suitable polynomial relationship between ? and CL and fit a curve to the data points by the least-squares method using (a) hand calculations and (b) Matlab programming Hint: A quadratic equation (parabola) y(x)-aa,x +a x' can be used in...
16. (8 points) Consider the following possible rough sketch of the graph of a polynomial function. Which of the following polynomial functions most closely matches the above graph? (a) plz) = (z + 4)(z + 2)(z-1)(z-3) (b) p@) = (z + 4)(z + 2)(3.? + 1) Clearly CIRCLE your answer, and below, use 1-2 sentences to JUSTIFY your answer, citing the specific features of the graph that distinguish your choice from the other choices.
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...
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...
Consider the following points. (-1, 5), (0, 0), (1, 1), (4, 58) (a) Determine the polynomial function of least degree whose graph passes through the given points. p(x) = (b) Sketch the graph of the polynomial function, showing the given points. y 2 3 4 2 3 -10 -20 -20 -30 -40 -40 -60 -50 -601 -80 у BOF у 60 50 60 40 40 30 20 20 10 х 2 3 4 2 3
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...
help wanted??
thank you
explain correctly
Problem 1 Use the trapezoidal rule technique to approximate the following integrals: a) 「(x2+1)dr(Note: use 0.5 increments forx) b) sina d INote: use a MATLAB function to subdivide the interval into eight equal parts) c e dx (Note: use 0.25 increments for x Problem 2 Use the Simpson's rule to evaluate the following integrals aDdr Problem 3: Given the polynomial: x3-6x2 + 30-0, Use MATLAB to find all roots of this polynomial. Use MATLAB's...
Matlab:
a) Write a program to compute the first-degree and third-degree
polynomials that fit the data, displaying the polynomial
coefficients. Remember to include text to describe the displayed
coefficients.
(b) Compute and display (including what the information is) the
sum of the squares for each curve fit.
(c) Plot the data and the two curve fits on a
single plot, for 101 values of A in the range 0 ?
A ? 9. Choose different line styles for each curve...
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