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Bisection method

Index Bisection method

The bisection method in mathematics is a root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. [1]

14 relations: Approximation error, Binary search algorithm, Bisection, Continuous function, Intermediate value theorem, Interval (mathematics), Lehmer–Schur algorithm, Mathematics, Nested intervals, Pseudocode, Rate of convergence, Real number, Root-finding algorithm, Zero of a function.

Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it.

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Binary search algorithm

In computer science, binary search, also known as half-interval search,logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array.

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Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Intermediate value theorem

In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval,, as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.

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Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

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Lehmer–Schur algorithm

In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Nested intervals

In mathematics, a sequence of nested intervals is understood as a collection of sets of real numbers such that each set is an interval of the real line, for n.

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Pseudocode

Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.

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Rate of convergence

In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Root-finding algorithm

In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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Bisection algorithm, Bisection search, Interval bisection, Interval halving, Interval halving converges linearly, Method of bisection.

References

[1] https://en.wikipedia.org/wiki/Bisection_method

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