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- W1570293671 abstract "In computational physics very often roots of a function have to be determined. A related problem is the search for local extrema which for a smooth function are roots of the gradient. In one dimension bisection is a very robust but rather inefficient root finding method. If a good starting point close to the root is available and the function smooth enough, the Newton–Raphson method converges much faster. Special strategies are necessary to find roots of not so well behaved functions or higher order roots. The combination of bisection and interpolation like in Dekker’s and Brent’s methods provides generally applicable algorithms. In multidimensions calculation of the Jacobian matrix is not always possible and Quasi-Newton methods are a good choice. Whereas local extrema can be found as the roots of the gradient, at least in principle, direct optimization can be more efficient. In one dimension the ternary search method or Brent’s more efficient golden section search method can be used. In multidimensions the class of direction set search methods is very popular which includes the methods of steepest descent and conjugate gradients, the Newton–Raphson method and, if calculation of the full Hessian matrix is too expensive, the Quasi-Newton methods." @default.
- W1570293671 created "2016-06-24" @default.
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- W1570293671 date "2013-01-01" @default.
- W1570293671 modified "2023-09-24" @default.
- W1570293671 title "Roots and Extremal Points" @default.
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- W1570293671 doi "https://doi.org/10.1007/978-3-319-00401-3_6" @default.
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