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Numerical method
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I. 20 points. USE 3 DECIMAL PLACES IN ALL CALCULATIONS. Given the following data, calculate f(2) ...
Given these data: x 1 2 3 5 7 8 f(x) 3 6 19 99 291...
Given these data: x 1 2 3 5 7 8 f(x) 3 6 19 99 291 444 a) Calculate f(4) using Newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy. What do your results indicate regarding the order of the polynomial used to generate the data in the table?
please help with #1 a and b. thank you Use the following data for all problems:...
please help with #1 a and b. thank you
Use the following data for all problems: The data below defines the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: T°C omg/L 0 8 16 14.621 11.843 9.870 24 32 40 8.418 7.305 6.413 a. Approximate o(19) using a 1st order Newton's interpolating polynomial. b. Approximate o(19) using a 2nd order Newton's interpolating polynomial. 2) Use linear algebra to find the coefficients of the 2nd order...
need help doing this in matlab. 1.2-1.4 Problem #1. For five data points listed in Table...
need help doing this in matlab. 1.2-1.4
Problem #1. For five data points listed in Table 1, you are asked to do the following: Write down the form of a Newton's interpolating polynomial function of 4th-order with five constants (b, i = 1:5). 1.2 Calculate the following three divided differences (Newton bracket) (showing the detailed steps and numbers on a white paper): [xy, x,]= [xx, x,]= S[X2, x3, x,]= Plot both the data points and the interpolating function by using...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the ...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
matlab The error function is a mathematical function that frequently arises in probability and statistics. It also c...
matlab
The error function is a mathematical function that frequently arises in probability and statistics. It also can show up in the solution to some partial differential equations, particularly those arising in heat and mass transfer applications. The error function is defined as 2 e-t dt picture attached This function is actually built-in to MATLAB as the command erf, and here we'll use that function to compute a "true value" with which we can compare results of two interpolation approaches....
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9....
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9. Determine the polynomial term corresponding to the data point f(3) 8. Be sure to simplify as much as possible. (Don't take time to write the other two terms.) (1 point)
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided difference...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
2. Please use 2 places of decimal for calculations. A. The following are a list of...
2. Please use 2 places of decimal for calculations. A. The following are a list of quantities of skirts sold weekly in the past ten weeks at & Co: 100, 125, 200, 100, 127, 300, 99, 200, 215, 225. Graph a histogram/boxplot to show these data. Explain/show how you get the numbers for the boxplot/histogram. B. The table below gives the prices of skirts at Jonathan & Co. and quantities sold in selected weeks. Calculate the mean and the standard...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 point...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 points of this function: 10.5403 2 -0.4161 6 0.9602 (a) (2 points) Calculate the quadratic Lagrange interpolating polynomial as the sum of the Lo(x), L1(x), L2(x) polynomials we defined in class. The final answer should be in the form P)a2 bx c, but with a, b, c known. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand...
matlab matlab For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a k...
matlab
matlab
For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error Consider the following mathematical function (Runge's function): 1+25r2 Write a function mfile that uses this formula to generate a set of data use those points along approaches outlined...
please help with #1 a and b. thank you
Use the following data for all problems: The data below defines the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: T°C omg/L 0 8 16 14.621 11.843 9.870 24 32 40 8.418 7.305 6.413 a. Approximate o(19) using a 1st order Newton's interpolating polynomial. b. Approximate o(19) using a 2nd order Newton's interpolating polynomial. 2) Use linear algebra to find the coefficients of the 2nd order...
need help doing this in matlab. 1.2-1.4
Problem #1. For five data points listed in Table 1, you are asked to do the following: Write down the form of a Newton's interpolating polynomial function of 4th-order with five constants (b, i = 1:5). 1.2 Calculate the following three divided differences (Newton bracket) (showing the detailed steps and numbers on a white paper): [xy, x,]= [xx, x,]= S[X2, x3, x,]= Plot both the data points and the interpolating function by using...
3. (30 points) Let f(x) = 1/x and data points Zo = 2, x,-3 and x2 = 4. Note that you can use the abscissae to find the corresponding ordinates (a) (8 points) Find by hand the Lagrange form, the standard form, and the Newton form of the interpolating polynomial p2(x) of f(x) at the given points. State which is which! Then, expand out the Newton and Lagrange form to verify that they agree with the standard form of p2...
matlab
The error function is a mathematical function that frequently arises in probability and statistics. It also can show up in the solution to some partial differential equations, particularly those arising in heat and mass transfer applications. The error function is defined as 2 e-t dt picture attached This function is actually built-in to MATLAB as the command erf, and here we'll use that function to compute a "true value" with which we can compare results of two interpolation approaches....
3) A 2nd-order Lagrange Interpolating Polynomial is to be fit to the following data points:(1)-1,1(2)4, 1(3)-9. Determine the polynomial term corresponding to the data point f(3) 8. Be sure to simplify as much as possible. (Don't take time to write the other two terms.) (1 point)
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i
+ 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1,
f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the
data point (0, 3), find a Newton form for the Lagrange polynomial
interpolating all 5 data points.
3. (25 pts) Let (r,, f()), 0,3, be data...
2. Please use 2 places of decimal for calculations. A. The following are a list of quantities of skirts sold weekly in the past ten weeks at & Co: 100, 125, 200, 100, 127, 300, 99, 200, 215, 225. Graph a histogram/boxplot to show these data. Explain/show how you get the numbers for the boxplot/histogram. B. The table below gives the prices of skirts at Jonathan & Co. and quantities sold in selected weeks. Calculate the mean and the standard...
3. Consider the function f(x) = cos(x) in the interval [0,8]. You are given the following 3 points of this function: 10.5403 2 -0.4161 6 0.9602 (a) (2 points) Calculate the quadratic Lagrange interpolating polynomial as the sum of the Lo(x), L1(x), L2(x) polynomials we defined in class. The final answer should be in the form P)a2 bx c, but with a, b, c known. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand...
matlab
matlab
For this problem you will test a few interpolation approaches for the application of generating interpolated data. We'll do this by interpolating data that is sampled from a known mathematical function. The same function can then be used to compute true values at the interpolated points to use in error Consider the following mathematical function (Runge's function): 1+25r2 Write a function mfile that uses this formula to generate a set of data use those points along approaches outlined...
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