BaseNumericalAnalysis

This C repository, developed during the course of AN410 Numerical Analysis - A.A.2019/19, is a collection of programs for scientific calculus application.

It follows a list of the main methods implemented:

Programs Implemented

• Direct methods for solving linear systems
  • Gauss Elimination
  • LU Factorization
    • Cholesky Factorization
    • Doolittle Factorization
  • QR factorization
• Iteratives methods for solving linear systems
  • Jacobi method
  • Gauss-Seidel method
  • Sor method
  • Richardson
• Recursive methods for function zeros
  • Bisection
  • Chord
  • Muller
  • Newton
  • Newton Quotient
  • Secantes
  • Steffensen
• Interpolation methods for function approximation over equidistant/chebyshev knots
  • Lagrange interpolate
  • Newton interpolate
  • Hermite interpolate
• Least-square method for function approximation
  • First Order Least-squares
  • Higher Order Least-Squares

Dependecies

Even if it is not necessary, an useful tool called by the program is GnuPlot. To change the path to the executable of GnuPlot it is necessary to change the macro defined in src/utils/an1.utils.h.

Structure of the Repository

• gnuplot-scripts: Contains the GnuPlot scripts called from inside the C code.
• results: Contains the computation output of the program.
• source: Contains all the default parsing .txt files.
• src: Source folder of the .c and .h files:
  • direct: direct methods implementation
  • function-zeros: function zeros evaluation methods implementation
  • interpolation: interpolation methods implementation
  • iteratives: iteratives methods implementation
  • utils: all the utilities usefull for the program
    • an1.utils.h
    • utils_functions.c
    • utils_matrices.c
    • utils_systems.c
    • utils_utility.c
    • utils_vectors.c

The file src/utils/an1.utils.h also declare all the macros used here also as global parameter.

Some of them could be modified in order to change the outputs:

Macro	Usage
lfpf	long float print format
flfpf	long float print format over files
gnuplot(x)	gnuplot application path
MAX_ATTEMPTs	max attempts for iterative methods
MAX_ERRs	max number of errors during choosing
ERR	default max error for approximations
MAX_POINTs	max number of data points that could be evaluated
CONST_DATA	number of data points for sample functions evaluation

Author

• Elia Onofri - Ln ([email protected])

Bibliography Link

• AN410 lecture notes by R. Ferretti;
• Matematica Numerica ed.3 by A. Quarteroni - R. Sacco - F. Saleri QSS08;