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  2. Newton's method in optimization - Wikipedia

    en.wikipedia.org/wiki/Newton's_method_in...

    In calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function, which are solutions to the equation =. However, to optimize a twice-differentiable f {\displaystyle f} , our goal is to find the roots of f ′ {\displaystyle f'} .

  3. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x 2 = a is equivalent to finding a root of the function f(x) = x 2 − a. The Newton iteration defined by this function is given by

  4. Newton polynomial - Wikipedia

    en.wikipedia.org/wiki/Newton_polynomial

    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 ...

  5. Polynomial root-finding algorithms - Wikipedia

    en.wikipedia.org/wiki/Polynomial_root-finding...

    Finding the root of a linear polynomial (degree one) is easy and needs only one division: the general equation + = has solution = /. For quadratic polynomials (degree two), the quadratic formula produces a solution, but its numerical evaluation may require some care for ensuring numerical stability.

  6. List of numerical analysis topics - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical_analysis...

    Order of accuracy — rate at which numerical solution of differential equation converges to exact solution; Series acceleration — methods to accelerate the speed of convergence of a series Aitken's delta-squared process — most useful for linearly converging sequences; Minimum polynomial extrapolation — for vector sequences; Richardson ...

  7. Method of dominant balance - Wikipedia

    en.wikipedia.org/wiki/Method_of_dominant_balance

    The method may be iterated to generate additional terms of an asymptotic expansion to provide a more accurate solution. [11] Iterative methods such as the Newton-Raphson method may generate a more accurate solution. [4] A perturbation series, using the approximate solution as the first term, may also generate a more accurate solution. [5]

  8. Gauss–Newton algorithm - Wikipedia

    en.wikipedia.org/wiki/Gauss–Newton_algorithm

    Note that quasi-Newton methods can minimize general real-valued functions, whereas Gauss–Newton, Levenberg–Marquardt, etc. fits only to nonlinear least-squares problems. Another method for solving minimization problems using only first derivatives is gradient descent. However, this method does not take into account the second derivatives ...

  9. Newton fractal - Wikipedia

    en.wikipedia.org/wiki/Newton_fractal

    The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(z) ∈ [z] or transcendental function. It is the Julia set of the meromorphic function z ↦ z − ⁠ p(z) / p′(z) ⁠ which is given by Newton's method.