4. For the following table, answer the questions.
(1) Find the cubic Newton’s interpolating polynomial using the first four data points and estimate the function value at x=2.5 with the interpolating polynomial.
(2) Find the quartic Newton’s interpolating polynomial using the five data points and estimate the function value at x=2.5 with the interpolating polynomial.
(3) Find the bases functions of Lagrange interpolation, Li(x) (i=1,2,…,5), and estimate the function value at x=2.5 with the Lagrange interpolating polynomial.
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4. For the following table, answer the questions. (1) Find the cubic Newton’s interpolating polynomial using...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5),...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5) (2,3,1)
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpo...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpolating polynomials, and use MATLAB to graph both the interpolating polynomials and the data points: a) The piecewise linear Lagrange interpolating polynomialx) b) The piecewise quadratic Lagrange interpolating polynomial q(x) c) Newton's divided difference interpolation pa(x) of degree s 4
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the e...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate...
6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate P(1): -1 2 f(x) f'(x -4 2 1 5 -4 f"(x) -12
6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate P(1): -1 2 f(x) f'(x -4 2 1 5 -4 f"(x) -12
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...
1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2;...
1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2; f(0) = 0; f(3) = 4 and f (7) = 7. (6 points)
question 3 please The first 5 questions refer to finding solutions to the equation exp(w) =...
question 3 please
The first 5 questions refer to finding solutions to the equation exp(w) = 3.8 ln(1+x). You will need to write it in the form f(x)-0, and use various root finding methods. 1. (10 pts) Plot the curves y- exp(Vx), and y 3.8 ln(1+x) on the same graph in the range 0 x 6. Read off intervals in which there are roots of the equation exp(k)- 3.8 In(1+x) Now find the roots to 6 decimal places using the...
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...
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...
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following interpolating polynomials, and use MATLAB to graph both the interpolating polynomials and the data points: a) The piecewise linear Lagrange interpolating polynomialx) b) The piecewise quadratic Lagrange interpolating polynomial q(x) c) Newton's divided difference interpolation pa(x) of degree s 4
Problem 2. Given the data points (xi. yi), with xi 2 02 4 yil 5 1 1.25 find the following...
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate P(1): -1 2 f(x) f'(x -4 2 1 5 -4 f"(x) -12
6. (25 pts) Find the osculating polynomial, P, interpolating the following table of data, and evaluate P(1): -1 2 f(x) f'(x -4 2 1 5 -4 f"(x) -12
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...
1. Using the Lagrange interpolation polynomial, estimate the value of f(4), knowing that f(-1) = 2; f(0) = 0; f(3) = 4 and f (7) = 7. (6 points)
question 3 please
The first 5 questions refer to finding solutions to the equation exp(w) = 3.8 ln(1+x). You will need to write it in the form f(x)-0, and use various root finding methods. 1. (10 pts) Plot the curves y- exp(Vx), and y 3.8 ln(1+x) on the same graph in the range 0 x 6. Read off intervals in which there are roots of the equation exp(k)- 3.8 In(1+x) Now find the roots to 6 decimal places using the...
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...
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...
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