Bisection
The video for Bisection can be https://youtu.be/MlP_W-obuNg. Example code is given in the FalsePosition.c file, written in C, which compares Bisection Method against False Position Method. More information can be found here.
The video for Generalized Bisection Method can be found here https://youtu.be/rMg61nfkZ3M. You can run the program online via repl.it. Code can also be found here. To run the program locally have Python installed (including numpy and matplotlib) then type python3 GeneralizedBisection.py. To create documentation use the command python -m pydoc -w GeneralizedBisection.
- "A two-dimensional analogue to the method of bisections for solving nonlinear equations" by Charles Harvey and Frank Stenger https://doi.org/10.1090/S0025-5718-1979-0521286-6
- "A three-dimensional analogue to the method of bisections for solving nonlinear equations" by Krzysztof Sikorski https://doi.org/10.1090/S0025-5718-1979-0521286-6
- "A bisection method for systems of nonlinear equations" by Eiger et. al. https://doi.org/10.1145/2701.2705
- "An efficient degree-computation method for a generalized method of bisection" by Baker Kearfott https://doi.org/10.1007/BF01404868
- "Abstract generalized bisection and a cost bound" by Baker Kearfott https://doi.org/10.1090/S0025-5718-1987-0890261-9
- "Solving systems of nonlinear equations using the nonzero value of the topological degree" by Michael N. Vrahatis https://doi.org/10.1145/50063.214384