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An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's 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.
Newton's method, in its original version, has several caveats: It does not work if the Hessian is not invertible. This is clear from the very definition of Newton's method, which requires taking the inverse of the Hessian. It may not converge at all, but can enter a cycle having more than 1 point. See the Newton's method § Failure analysis.
Composed in 1669, [4] during the mid-part of that year probably, [5] from ideas Newton had acquired during the period 1665–1666. [4] Newton wrote And whatever the common Analysis performs by Means of Equations of a finite number of Terms (provided that can be done) this new method can always perform the same by means of infinite Equations.
A newton is defined as 1 kg⋅m/s 2 (it is a named derived unit defined in terms of the SI base units). [1]: 137 One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, [1] is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated using Newton's ...
Sometimes the names of units obscure the fact that they are derived units. For example, a newton (N) is a unit of force, which may be expressed as the product of mass (with unit kg) and acceleration (with unit m⋅s −2). The newton is defined as 1 N = 1 kg⋅m⋅s −2.
For Newton number, see also Kissing number in the sphere packing problem. For use in arithmetic and algebra, see Exponentiation . The power number N p (also known as Newton number ) is a commonly used dimensionless number relating the resistance force to the inertia force .
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constrained nonlinear least-squares problems.