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Question 3 (a) Consider the data. 00 0 25 0.5 05 () Construct the divaded difference's table for the data (u) Co...
Question 3 (a) Consides the data 00 025 05 05 (2) (i) Cousta uct the divided difference's table for the data (u...
Question 3 (a) Consides the data 00 025 05 05 (2) (i) Cousta uct the divided difference's table for the data (u) Construct the Newton forin of the polynomial p(a) of lowest degree that ntes polates /() at these points (3) (un) Suppose that these data were generated by the fun ton cos 22 )= 1+ 2 Use the nest term rule to appioumate the erior lp()- /() over the inter val [0,0 5 (3) Your anwer should be a...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Co...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Consrwet the Newton forsn of the polynomsnl p(a) of lowe-t degree that tes polates /) nt these potse () (n) Suppose that these data wese generated by thhe fumton cos 21 J)-1 2 Use the nest term rule to appOInate the eror Ipl)-f)over the intessal 0,05 Your anves should be a numbes (3) (b) Let f)Co +ealco...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a functi...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
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...
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 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.
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
Consider the following set of data x f(x) 3 6 4 3 5 8 1. Use...
Consider the following set of data x f(x) 3 6 4 3 5 8 1. Use and order Newton polynomial to find f (4.5). 2. Use and order Lagrange polynomial to find f (4.5). You should get the same answer using both methods they are just different representations of a quadratic (i.e., 2nd order) interpolating polynomial.
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...
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...
its a numerical analysis question QUESTION 4 (a) A natural cubic spline that fits the data...
its a numerical analysis question
QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
Due by 12:00 noon, today 05/12/20. : CU{co} → Problem 1. Consider the Möbius transformation CU{o}...
Due by 12:00 noon, today 05/12/20. : CU{co} → Problem 1. Consider the Möbius transformation CU{o} defined by S(z) = 171 (i) Compute f(1), f(), f(-1), f(-i). (ii) Show that for 2 = ei, where 0 ER, f(x) is real or oo, that is f(el) E RU{0} (iii) Let D = {z zz < 1} denote the open unit disc and H = {z | Im(2) >0} denote the upper half plane. Show that f takes D onto H. (iv)...
Question 3 (a) Consides the data 00 025 05 05 (2) (i) Cousta uct the divided difference's table for the data (u) Construct the Newton forin of the polynomial p(a) of lowest degree that ntes polates /() at these points (3) (un) Suppose that these data were generated by the fun ton cos 22 )= 1+ 2 Use the nest term rule to appioumate the erior lp()- /() over the inter val [0,0 5 (3) Your anwer should be a...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Consrwet the Newton forsn of the polynomsnl p(a) of lowe-t degree that tes polates /) nt these potse () (n) Suppose that these data wese generated by thhe fumton cos 21 J)-1 2 Use the nest term rule to appOInate the eror Ipl)-f)over the intessal 0,05 Your anves should be a numbes (3) (b) Let f)Co +ealco...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
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...
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.
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
Consider the following set of data x f(x) 3 6 4 3 5 8 1. Use and order Newton polynomial to find f (4.5). 2. Use and order Lagrange polynomial to find f (4.5). You should get the same answer using both methods they are just different representations of a quadratic (i.e., 2nd order) interpolating polynomial.
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...
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...
its a numerical analysis question
QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
Due by 12:00 noon, today 05/12/20. : CU{co} → Problem 1. Consider the Möbius transformation CU{o} defined by S(z) = 171 (i) Compute f(1), f(), f(-1), f(-i). (ii) Show that for 2 = ei, where 0 ER, f(x) is real or oo, that is f(el) E RU{0} (iii) Let D = {z zz < 1} denote the open unit disc and H = {z | Im(2) >0} denote the upper half plane. Show that f takes D onto H. (iv)...
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