Inverse quadratic interpolation

Inverse quadratic interpolation is a numerical method used to approximate the root of a function. It is a combination of the bisection, secant, and inverse quadratic interpolation methods. The inverse quadratic interpolation method involves using a quadratic equation to estimate the location of the root, based on three known points on the function.From: A Concise Introduction to Numerical Analysis [2018], Discrete bit-loading for OFDM systems under BER-constraint and imperfect CSI [2022]

Nonlinear Algebraic Equations

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Published in Niket S. Kaisare, Computational Techniques for Process Simulation and Analysis Using MATLAB®, 2017

Niket S. Kaisare

Brent’s method is more popularly known as inverse quadratic interpolation, because a quadratic function of Equation 6.16 is employed for the next guess. It is called inverse quadratic because here x is interpolated as a function of g(i)’s.

Discrete bit-loading for OFDM systems under BER-constraint and imperfect CSI

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Published in International Journal of Electronics Letters, 2022

Hocine Ait Saadi, Samir Dahmani, Mountassar Maamoun

To resolve the non linear optimisation problem in (5), we set and the Brent-Dekker method is used (Brent, 1973). This method combines the bisection, secant and inverse quadratic interpolation methods. However, in addition to significant computational complexity, the values obtained are not integer numbers and of infinite granularity, and therefore not useful in practice where it is necessary to load integer bits belonging to a set of finite values. This constraint is supported by the algorithm proposed in the next section.

Inverse quadratic interpolation

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Nonlinear Algebraic Equations

Discrete bit-loading for OFDM systems under BER-constraint and imperfect CSI