QuadSimp

The Problem

Numerical methods courses require students to solve quadratic spline interpolation and simplex method problems by hand — tedious, error-prone calculations that obscure the underlying concepts. A visual, interactive tool could help students verify their work and build intuition.

The Solution

I built QuadSimp as an RShiny web application with two modules.

• Quadratic spline interpolation — Input data points, and the app computes and visualizes the piecewise quadratic spline with step-by-step coefficient derivation.
• Simplex method solver — Handles both generic LP problems and transportation problems. Displays each pivot step, the tableau state, and the optimal solution.
• Interactive UI — Users can adjust inputs and immediately see how the solution changes, building intuition for how the algorithms work.

What Went Wrong

The simplex solver would enter infinite cycling on certain degenerate LP problems where multiple variables had equal ratios during pivot selection.

The fix: I implemented Bland's rule for pivot selection — always choosing the variable with the smallest index among tied candidates — which guarantees termination and prevents cycling in degenerate cases.

Results

• Step-by-step visualization of numerical method algorithms
• Handles both generic and transportation simplex problems
• Bland's rule prevents cycling on degenerate inputs