Bisection method
In Mathematics, the bisection method is a straightforward technique to find numerical solutions of an equation with one unknown. Bisection method is the simplest among all the numerical schemes to solve the transcendental equations. This scheme is based on the intermediate value theorem for continuous functions. The Bisection Method is a successive approximation method that narrows down an interval that contains a root of the function f(x) It is a simple method, and it is relatively slow. The bisection method is also known as interval halving method, root-finding method, binary search method or dichotomy method.
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Newton-raphson method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named
after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces
successively better approximations to the roots (or zeroes) of a real-valued function.
The Newton-Raphson method (also known as Newton's method) is a way to quickly find a
good approximation for the root of a real-valued function f(x)=0. It uses the idea
that a continuous and differentiable function can be approximated by a straight line
tangent to it.
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Secant method
The secant method is very similar to the bisection method except instead of dividing each interval by choosing the midpoint the secant method divides each interval by the secant line connecting the endpoints. The secant method always converges to a root of f(x)=0 provided that f(x) is continuous on [a,b] and f(a)f(b) < 0.
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Regula-falsi method
Regula Falsi method or the method of false position is a numerical method for solving an equation in one unknown. It is quite similar to bisection method algorithm and is one of the oldest approaches. It was developed because the bisection method converges at a fairly slow speed. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome.
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Fixed point iteration method
Fixed point iteration is method of computing fixed points of iterated functions. More specifically, given a function f(x) defined on the real numbers with real values and given a point x0 in the domain of f(x), the fixed point iteration is which gives rise to the sequence which is hoped to converge to a point x. If f(a) is continuous then one can prove that the obtained x is a fixed point of f(x), i.e., f(x) = x.
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Forward
- Forward
- Backward
- Lagrange
Interpolation
Interpolation is a method of finding new data points within the range of a discrete set of known data points. In other words, interpolation is the technique to estimate the value of a mathematical function, for any intermediate value of the independent variable. Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points in terms of the first value and the powers of the forward difference.
Interpolation is a method of finding new data points within the range of a discrete set of known data points. In other words, interpolation is the technique to estimate the value of a mathematical function, for any intermediate value of the independent variable. For interpolating the value of the function y=f(X) near the end of table of values, and to extrapolate value of the function a short distance forward from Yn, Newton backward interpolation is used.
Interpolation is a method of finding new data points within the range of a discrete set of known data points. In other words, interpolation is the technique to estimate the value of a mathematical function, for any intermediate value of the independent variable. Lagrange polynomials are used for polynomial interpolation. For a given set of distinct points xj and numbers yj. Lagrange’s interpolation is also an Nth degree polynomial approximation to f(x). The Lagrange interpolation formula is a way to find a polynomial which takes on certain values at arbitrary points. It is very useful method for entries and attributes unequally spaced.
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Divided difference method
Interpolation is a method of finding new data points within the range of a discrete set of known data points. In other words, interpolation is the technique to estimate the value of a mathematical function, for any intermediate value of the independent variable. Newton’s divided difference interpolation formula is a interpolation technique used when the interval difference is not same for all sequence of values.