We propose an algorithm that estimates the real roots of differentiable functions on closed intervals. Then, we extend this algorithm to real differentiable functions that are dominated by a polynomial. For each starting point, our method converges to the nearest root to the right or left hand side of that point. Our algorithm can look for missed roots as well and theoretically it misses no root. Furthermore, we do not find the roots by randomly chosen initial guesses. The iterated sequences in our algorithms converge linearly. Therefore, the rate of convergence can be accelerated considerably to make it comparable to Newton-Raphson and other high-speed methods. We have illustrated our algorithms with some concrete examples. Finally, the pseudo-codes of the related algorithms are presented at the end of this manuscript.
Khandani, H. (2023). New algorithms to estimate the real roots of differentiable functions and polynomials on a closed finite interval. Journal of Mathematical Modeling, 11(4), 631-647. doi: 10.22124/jmm.2023.22967.2040
MLA
Hassan Khandani. "New algorithms to estimate the real roots of differentiable functions and polynomials on a closed finite interval". Journal of Mathematical Modeling, 11, 4, 2023, 631-647. doi: 10.22124/jmm.2023.22967.2040
HARVARD
Khandani, H. (2023). 'New algorithms to estimate the real roots of differentiable functions and polynomials on a closed finite interval', Journal of Mathematical Modeling, 11(4), pp. 631-647. doi: 10.22124/jmm.2023.22967.2040
VANCOUVER
Khandani, H. New algorithms to estimate the real roots of differentiable functions and polynomials on a closed finite interval. Journal of Mathematical Modeling, 2023; 11(4): 631-647. doi: 10.22124/jmm.2023.22967.2040
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