@@ -67,12 +67,12 @@ Procedure | Description | Reference
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[ ` regula_falsi ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/regula_falsi.html ) | Classic regula falsi method | ?
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[ ` muller ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/muller.html ) | Improved Muller method (for real roots only) | [ Muller (1956)] ( https://www.ams.org/journals/mcom/1956-10-056/S0025-5718-1956-0083822-0/S0025-5718-1956-0083822-0.pdf )
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[ ` brent ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/brent.html ) | Classic Brent's method (a.k.a. Zeroin) | [ Brent (1971)] ( https://maths-people.anu.edu.au/~brent/pd/rpb005.pdf )
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- [ ` brenth ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/brenth.html ) | SciPy variant of ` brent ` | [ SciPy ] ( https://github.com/scipy/scipy/ )
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- [ ` brentq ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/brentq.html ) | SciPy variant of ` brent ` | [ SciPy ] ( https://github.com/scipy/scipy/ )
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+ [ ` brenth ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/brenth.html ) | [ SciPy] ( https://github.com/scipy/scipy/ ) variant of ` brent ` | [ Brent (1971) ] ( https://maths-people.anu.edu.au/~brent/pd/rpb005.pdf )
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+ [ ` brentq ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/brentq.html ) | [ SciPy] ( https://github.com/scipy/scipy/ ) variant of ` brent ` | [ Brent (1971) ] ( https://maths-people.anu.edu.au/~brent/pd/rpb005.pdf )
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[ ` illinois ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/illinois.html ) | Illinois method | [ Dowell & Jarratt (1971)] ( https://personal.math.ubc.ca/~loew/mech2/Dowell+Jarratt.pdf )
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[ ` pegasus ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/pegasus.html ) | Pegasus method | [ Dowell & Jarratt (1972)] ( https://link.springer.com/article/10.1007/BF01932959 )
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[ ` anderson_bjorck ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/anderson_bjorck.html ) | Anderson-Bjorck method | [ King (1973)] ( https://link.springer.com/article/10.1007/BF01933405 )
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- [ ` anderson_bjorck_king ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/anderson_bjorck_king.html ) | a [ variant] ( https://link.springer.com/content/pdf/bbm%3A978-3-642-05175-3%2F1.pdf ) of ` anderson_bjorck ` | [ King (1973)] ( https://link.springer.com/article/10.1007/BF01933405 )
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+ [ ` anderson_bjorck_king ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/anderson_bjorck_king.html ) | A [ variant] ( https://link.springer.com/content/pdf/bbm%3A978-3-642-05175-3%2F1.pdf ) of ` anderson_bjorck ` | [ King (1973)] ( https://link.springer.com/article/10.1007/BF01933405 )
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[ ` ridders ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/ridders.html ) | Classic Ridders method | [ Ridders (1979)] ( https://cs.fit.edu/~dmitra/SciComp/Resources/RidderMethod.pdf )
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[ ` toms748 ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/toms748.html ) | Algorithm 748 | [ Alefeld, Potra, Shi (1995)] ( https://dl.acm.org/doi/abs/10.1145/210089.210111 )
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[ ` chandrupatla ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/chandrupatla.html ) | Hybrid quadratic/bisection algorithm | [ Chandrupatla (1997)] ( https://dl.acm.org/doi/10.1016/S0965-9978%2896%2900051-8 )
@@ -82,6 +82,7 @@ Procedure | Description | Reference
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[ ` itp ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/itp.html ) | Interpolate Truncate and Project method | [ Oliveira & Takahashi (2020)] ( https://dl.acm.org/doi/abs/10.1145/3423597 )
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[ ` barycentric ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/barycentric.html ) | Barycentric interpolation method | [ Mendez & Castillo (2021)] ( https://www.researchgate.net/publication/352162661_A_highly_efficient_numerical_method_to_solve_non-linear_functions_using_barycentric_interpolation )
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[ ` blendtf ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/blendtf.html ) | Blended method of trisection and false position | [ Badr, Almotairi, Ghamry (2021)] ( https://www.mdpi.com/2227-7390/9/11/1306/htm )
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+ [ ` modab ` ] ( https://jacobwilliams.github.io/roots-fortran/proc/modab.html ) | Modified Anderson-Bjork | [ Ganchovski & Traykov (2023)] ( https://iopscience.iop.org/article/10.1088/1757-899X/1276/1/012010 )
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In general, all the methods are guaranteed to converge. Some will be more efficient (in terms of number of function evaluations) than others for various problems. The methods can be broadly classified into three groups:
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