Numerical Analysis

Input File Format

Both xValues.dat or yValues.dat must follow this format:

• The first value in the file represents the number of data points.
• The following values are the respective x or y coordinates.

Non-Linear Equations

Use the following command to compile the code:

gcc secant.c -lm -o secant.out

Run:

./secant.out 10 

Note: The number 10 represents the number of iterations.

Methods for Solving Systems of Equations

use this command to compile the code:

gcc jacobian.c -lm -o jacobian.out

Run:

./jacobian.out coefficients.dat constantTerms.dat

Note: Ensure that coefficients.dat and constantTerms.dat are present in the directory with the program and the first value in the file represents the number of elements.

Interpolation

Lagrange

Compilation and Execution

Simple version

gcc lagrange.c -o lagrange

Run:

./lagrange xValues.dat yValues.dat

Debug mode (with additional output for debugging):

gcc lagrange.c -D DEBUG -o lagrange

Run:

./lagrange xValues.dat yValues.dat 

Multi-threaded version

gcc lagrangeWithThreads.c -lm -o lagrangeThreads

Run:

./lagrangeThreads 2 xValues.dat yValues.dat

Note: num_threads specifies the number of threads to use (first argument).

Note: Ensure that xValues.dat and yValues.dat are present in the directory with the program.

System of Equations Solver (SEL)

The program solves a system of linear equations using the Gauss-Seidel method and prints the corresponding interpolating polynomial

Compilation

gcc sel.c -lm -o sel.out

Run:

./sel.out x.dat fx.dat

Note: Ensure that x.dat and fx.dat are present in the directory with the program and used the correct format.

Note: The program internally calls exec to run Gauss-Seidel and print the results (in Gauss-Seidel).

Newton’s Polynomial Interpolation

It calculates the interpolating polynomial using the Newton form and can be used to estimate the function polynomial.

Compilation

gcc newton_points.c -o newton.out

Run:

./newton.out x.dat fx.dat

Note: Ensure that x.dat and fx.dat are present in the directory with the program and used the correct format.