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Can you do my numerical analysis assignment based on interpolation?

Interpolation is an important concept in numerical analysis. Any mathematics students who want to pass their course with flying colors must be well-versed in interpolation. Quite often, several scholars flock to our website with "do my numerical analysis assignment based on interpolation" requests. If you are also stuck with an interpolation assignment, then you would be happy to know that we have got you covered.

What is interpolation in numerical analysis?

In many cases, functions may not be explicitly available but only nodes, pivotal points, or tabular points (values of the function at a set of points). Interpolation is the technique of finding the value of the function at any non-tabular point. It is done by estimating the needed function using simpler functions like polynomials. When estimating polynomials, we assume that the data is exact at (n+1) tabular points, then generate an Nth degree polynomial that cuts across the (n+1) points. Should the given data has some errors, then expect the errors to reflect on the corresponding estimated function. If you want to generate more accurate functions, then you can use:

• Splines polynomial
• Chebicheve polynomial
• Legender polynomial
• Hermite polynomial

Polynomials of degree N or less are widely used because they are easy to develop. They are also useful in explaining numerical integrals and differentiation.

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Stuck with finding the roots of nonlinear equations problem? Avail help with numerical analysis assignment from us

Are you worried because you cannot solve your finding roots of nonlinear equations assignment? Our help with numerical analysis assignment is what you need. There are many methods of solving for roots of nonlinear equations with one independent variable. Our professionals are acquainted with methods like:

Bisection method: This method is sometimes called the binary search method. It is one of the simplest methods of finding the root of a nonlinear equation with a single unknown variable. The other advantage of this method is that the root will always converge as long as it is bounded by the interval [a, b]. The bisection method is often used to get an initial rough approximation of a root. To get a better approximation of the root, it must be combined with a method that has a faster convergence

Newton-Raphson: The Newton-Raphson method sometimes just called the Newton method suits problems where a function of a single variable is mathematically-defined and you can easily evaluate the derivative of the function. This method estimates a function by its tangent line at a point. This is done to get better estimates of the root successively. Newton's method boasts a strong convergence property. This makes it the root-finding method of choice for functions with a derivative that is continuous near the root.

Secant method: While the Newton-Raphson method for root finding has strong convergence properties, its evaluation of f’(x) can sometimes be messy. A slight variation is required to circumvent this derivative calculation. The introduction of this variation creates a technique known as the secant method. The major problem with this method is that the algorithm is not guaranteed to converge for functions that are not sufficiently continuous. To guarantee convergence, but at a slower rate, a slight modification called the false position method can be made to the secant method.

Hybrid methods: Hybrid methods of finding the root of nonlinear equations simply combine any two or more methods to come up with a robust method. For instance, Brent’s method gets near the root using the bisection method and fine-tune it for faster convergence using the secant method.

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