Question

Write 10-15 applications of each.
(note formulas are not required, just applications)

1-Newton's Raphson Method
2-Langrange Interpolation polynomial
3-Newton Divided Difference

10-15 applications of 1st topic
10 - 15 applications of 2nd topic
10-15 applications of 3rd topic

Answer 1

Newton's Raphson Method

1) We use to find a minimum/maximum of a function  f(x). Local minima and maxima can be found by applying Newton's method to the derivative. The iteration becomes:

2) We can find the multiplicative inverses of numbers and power series by this method.

3) The transcendental equations also can be solved by using this method. Suppose we are given the equation g(x)=h(x)

where g(x),h(x) are transcendental functions. Then we can write f(x)=g(x)-h(x). The values of x are then the roots of f (x) which solve the original equation, can be found via Newton's method.

4) The Newton-Raphson Method in a Voice Localization System.

5) The Newton Raphson Method To compute the  non-linear models.

6) Newton-Raphson method is extensively used for analysis of flow in water distribution networks.

7) By this method we can also analyse the flow in large size networks.

8) It is used in the context of non-linear finite element analysis based on quasi-static problems in solid mechanics.

9) Newton's method is applied to the ratio of Bessel functions in order to obtain its root.

10) In a SDFEM for inviscid Burgers equation.

Langrange Interpolation polynomial

1) On analysing flavonoid of tempe.

2) Efficient Algorithms and Structures for Fractional Delay Filtering Based on Lagrange Interpolation.

3) For a signal reconstruction in event-based Generalized Predictive Control.

4)  Lagrange interpolation to compute the numerical solutions of differential equations.

5) To compute the numerical solutions of integral equations.

6) It is also useful to compute the solutions of integro-differential equations.

7) Use of Lagrange polynomials include the Newton–Cotes method of numerical integration.

8) Used in Shamir's secret sharing scheme in cryptography.

9) The Lagrangian interpolation to find estimates from tables where the entries are sparse, exact and the behavior being described is nonlinear.

10)  To fit a polynomial through them and determine values of dependent variables at intermediate points where data is not given.

Newton Divided Difference

1) This method can be used to calculate the coefficients in the interpolation polynomial in the Newton form.

2) Determination of a matrix function using the divided difference method.

3) Modeling of performance and retarder chart of off-highway truck by this method.

4) To compute the tables of logarithms.

5) We can also use this in computing the tables for trigonometric functions.

6) We can represent the partial fractions using the expanded form of divided differences.