Conjugate Gradient - Interactive Visualization

Conjugate gradient solves Ax=b (or equivalently minimizes a quadratic) in at most n steps for an n-dimensional problem. The key insight: CG search directions are conjugate (A-orthogonal) - each step corrects only what previous steps left uncorrected, without undoing prior progress. This is why CG needs only 2 steps for 2D, while steepest descent zigzags indefinitely.

• Watch CG reach minimum in exactly 2 steps on a 2D quadratic
• Watch steepest descent zigzag along the same problem
• Adjust condition number κ to see how CG convergence degrades
• See both paths animated simultaneously on elliptical contours
• Foundation for solving large sparse linear systems in scientific computing and ML

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.