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Ogbereyivwe O, Umar S S. Modified Householder Iterative Scheme requiring no Function Derivative for Solving Nonlinear Equations.. MACO 2022; 3 (2) : 8
URL: http://maco.lu.ac.ir/article-1-124-en.html
URL: http://maco.lu.ac.ir/article-1-124-en.html
Abstract: (839 Views)
The Householder iterative scheme (HIS) for determining solution of equations
that are nonlinear have existed for over fifty decades and have enjoyed several modifications
in literature. However, in most HIS modifications, they usually require function derivative
evaluation in their implementation. Obtaining derivative of some functions is difficult and in
some cases, it is not achievable.To circumvent this setback, the divided difference operator
was utilised to approximate function derivatives that appear in the scheme. This resulted
to the development of a new variant of the HIS with high precision and require no function
derivative. The theoretical convergence of the new scheme was established using Taylor’s
expansion approach. From the computational results obtained when the new scheme was
tested on some non-linear problems in literature, it performed better than the Householder
scheme.
that are nonlinear have existed for over fifty decades and have enjoyed several modifications
in literature. However, in most HIS modifications, they usually require function derivative
evaluation in their implementation. Obtaining derivative of some functions is difficult and in
some cases, it is not achievable.To circumvent this setback, the divided difference operator
was utilised to approximate function derivatives that appear in the scheme. This resulted
to the development of a new variant of the HIS with high precision and require no function
derivative. The theoretical convergence of the new scheme was established using Taylor’s
expansion approach. From the computational results obtained when the new scheme was
tested on some non-linear problems in literature, it performed better than the Householder
scheme.
Article number: 8
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