Numerical Methods · MEIE4183 · Fall 2024
Brief
The point of the project was to implement the methods, not to lean on MATLAB’s built-in solvers: write each algorithm from its definition, run it on engineering data, and check the result against a known answer. The work spans seven problems covering the four pillars of a numerical-methods course — root-finding, linear systems, curve fitting, and integration.
Root-Finding
Nonlinear roots are solved several ways and compared for convergence: the bisection method (guaranteed but slow), fixed-point iteration, and the secant method (faster, and no derivative required). Each routine tracks its own iteration count and approximate relative error down to a set tolerance.
Linear Systems
Systems of equations are solved with Gauss elimination with partial pivoting, LU decomposition, and the iterative Gauss–Seidel method, plus a routine that uses the LU factors to form a full matrix inverse. Pivoting and iteration behaviour are checked against MATLAB’s reference results.
Fitting & Interpolation
A multiple linear regression routine fits a response to two predictors through the
normal equations (B = (XᵀX)⁻¹ XᵀY) and reports the coefficients, predictions, and
residuals. A third-order Lagrange interpolation estimates a thermistor’s resistance
between calibration points — for example, the resistance at 33 °C from a four-point
resistance–temperature table.
Integration
Definite integrals are evaluated with the composite Simpson’s 1/3 rule, choosing the number of intervals to balance truncation error against effort.
Value
The result is a small library of trustworthy, well-understood routines — the same methods that sit underneath the control, signal-processing, and modelling work elsewhere in this portfolio. Implementing them from first principles turns their failure modes — pivoting, convergence, step size — into something concrete rather than abstract.