Implementation of Broyden's method

This project was an excercise for the lecture Numerical Mathematics for Bachelor students by Prof. Dr. Blank at the University of Regensburg in 2014. It implements Broyden's method for approximating roots of functions in k variables.

Compilation

For compilation you need gcc and make. Then call

make

Functionality

The programm broyden_method will offer a couple of example functions to choose from (see broyden_functions.h for documentation). You can then enter start values (start point and your guess for the derivation at that point) and other parameters. I recommend taking the default.

It will print the steps into OUTPUT_FILE (see broyden_file.h; currently broyden_method_output.txt). If possible, an approximation result for a root ist printed to the console.

Structure of the Files

Mind the comments in the source files that try to describe the functionality.

• Broyden's method: broyden_method.*
• Matrix operations (addition, multiplication, memory allociation): matrix_operations.*
• Solution of linear equation systems (with LU decomposition; see also here): solve_equation.*
• Example functions to choose from: broyden_functions.* (see also FUNCTION_OPTIONS* in broyden_input.h)
• Main function: broyden_main.*
• File-/Terminal-IO: broyden_file.*, broyden_input.*, broyden_output.*
• Build helper: Makefile, broyden.deps (automatically generated)