A new method to solve non-linear equations

A new iterative method to find the real roots of a single variable function ⨍( x) = 0 is discussed. It needs an interval which contains exactly one root to start the iterations. It transforms ⨍( x) = 0 to the form g( x) = c. Depending on c the method converges to the root either quadratically or lin...

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Bibliographic Details
Published in:Information processing letters 1994-04, Vol.50 (2), p.75-79
Main Authors: Sony Roy, T., Athithan, G., Ganagi, M.S., Sivasankara Reddy, A.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation
Computer science
control theory
systems
Convergence
Exact sciences and technology
Mathematical models
Non-linear equations
Studies
Theoretical computing
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Summary:A new iterative method to find the real roots of a single variable function ⨍( x) = 0 is discussed. It needs an interval which contains exactly one root to start the iterations. It transforms ⨍( x) = 0 to the form g( x) = c. Depending on c the method converges to the root either quadratically or linearly. Conditions for quadratic and linear convergence are given. The method is interesting in the sense that construction of the successive approximation to the root is based only on the previous approximation. Hence, it needs the minimal amount of memory. Some numerical examples are also presented.
ISSN:0020-0190
1872-6119
DOI:10.1016/0020-0190(94)00011-5