Prove that the algorithm for computing the coefficients in the Newton form of the interpolating polynomial...

Prove that the algorithm for computing the coefficients in the Newton form of the interpolating polynomial involves n^2 long operations (multiplication and division).

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Colby Messinger answered 8 months ago

build an excel sheet to calculate the coefficients of the third order Newton interpolating polynomial,and solve...

build an excel sheet to calculate the coefficients of the third order Newton interpolating polynomial,and solve it for any point x, please solve it by excel and i need the file thanks in advance

Prove that every polynomial having real coefficients and odd degree has a real root

Problem: Prove that every polynomial having real coefficients and odd degree has a real root This is a problem from a chapter 5.4 'applications of connectedness' in a book 'Principles of Topology(by Croom)' So you should prove by using the connectedness concept in Topology, maybe.

5.1 Using the method of undetermined coefficients, derive aninterpolation polynomial f(x) of the form "a...

Using the method of undetermined coefficients, derive an interpolation polynomial f(x) of the form "a +bx", for the following data. Determine the interpolation value of f(0.52).x 0.45 0.55 0.65 0.75y 0.075 0.136 0.227 0.372

Find the Chebyshev interpolation nodes on the interval [4,12] for an interpolating polynomial of degree 5

Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial...

Consider polynomial interpolation of the function f(x)=1/(1+25x^2) on the interval [-1,1] by (1) an interpolating polynomial determined by m equidistant interpolation points, (2) an interpolating polynomial determined by interpolation at the m zeros of the Chebyshev polynomial T_m(x), and (3) by interpolating by cubic splines instead of by a polynomial. Estimate the approximation error by evaluation max_i |f(z_i)-p(z_i)| for many points z_i on [-1,1]. For instance, you could use 10m points z_i. The cubic spline interpolant can be determined in...

Below is the graph of a polynomial function f with real coefficients.

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of fare shown in the graph. (a) The function f is increasing over which intervals? Choose all that apply. (-∞ , -8) (-8, -5) (-8, -2) (-2, 3) (7, 9) (9, ∞) (b) The function f has local maxima at which x-values? If there is more than one value separate them with commas. (c) What...

Q11: Use the Lagrange interpolating polynomial of degree three or less and four-digit chopping arithmetic to...

Q11: Use the Lagrange interpolating polynomial of degree three or less and four-digit chopping arithmetic to approximate cos 0.750 using the following values. Find an error bound for the approximation. cos 0.698 = 0.7661 ,cos 0.733 = 0.7432 cos 0.768 = 0.7193 cos 0.803 = 0.6946.

In this assignment, you will implement a Polynomial linked list, the coefficients and exponents of the...

In this assignment, you will implement a Polynomial linked list, the coefficients and exponents of the polynomial are defined as a node. The following 2 classes should be defined.

Compute the quartic interpolating polynomial for the Hermite interpolation problem p(0) = 2, p'(0) = -9...

Compute the quartic interpolating polynomial for the Hermite interpolation problem p(0) = 2, p'(0) = -9 p(1) = -4, p'(1) = 4 p(2) = 44 with respect to the Newton basis. Compute the divided differences. Find a quintic interpolating polynomial that additionally satisfies p(3) = 2.

Implement a class Polynomial that uses a dynamic array of doubles to store the coefficients for...

Implement a class Polynomial that uses a dynamic array of doubles to store the coefficients for a polynomial. Much of this work can be modelled on the C++ dynamic array of ints List that we discussed in class. This class does not need the method the overloaded += operator. Your class should have the following methods: Write one constructor that takes an integer n for the degree of a term and a double coefficient c for the coefficient of the...

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