Worksheets in MATLAB – Holistic Numerical Methods

Introduction to Scientific Computing

Measuring Errors

True Error [MATLAB] Approximate Error [MATLAB]

Binary Representation

Decimal to binary representation [MATLAB] Binary to decimal representation [MATLAB]

Measuring Errors

Decimal to floating point representation [MATLAB] Binary to floating point representation [MATLAB]

Propagation of Errors

Propagation of Errors [MATLAB]

Differentiation

Continuous Functions

Forward Divided Difference [MATLAB] Backward Divided Difference [MATLAB] Central Divided Difference [MATLAB] Continuous functions Second Order Derivative [MATLAB]

Discrete Data

Discrete functions [MATLAB]

Nonlinear Equations

Bisection Method

Method [MATLAB] Convergence [MATLAB] Pitfall: Slow convergence of bisection method simulation [MATLAB]

Newton-Raphson Method

Method [MATLAB] Convergence [MATLAB] Pitfall: Division by zero [MATLAB] Pitfall: Slow Convergence at Inflection Points [MATLAB] Pitfall: Root jumps over several roots [MATLAB] Pitfall: Roots oscillates around local maxima and minima [MATLAB]

Secant Method

Simulation of secant method [MATLAB] Convergence Simulation of secant method [MATLAB] Pitfall: Division by zero in secant method simulation [MATLAB] Pitfall: Root jumps over several roots in secant method [MATLAB]

Simultaneous Linear Equations

Gaussian Elimination

Method [MATLAB]

Gauss-Seidel Method

Method [MATLAB] Convergence [MATLAB]

LU Decomposition

Method [MATLAB]

Interpolation

Direct Method

Method [MATLAB]

Newton’s Divided Difference Method

Method [MATLAB]

Lagrange Method

Method [MATLAB]

Spline Method

Method [MATLAB]

Regression

Linear Regression

Method [MATLAB]

Nonlinear Regression

Without Data Linearization [MATLAB] With Data Linearization [MATLAB] Polynomial Regression [MATLAB] Comparing with and without Data Linearization [MATLAB]

Adequacy of a Regression Model

Adequacy [MATLAB]