conjugate-gradient-methods

Shows CG as iterative minimization of an SPD quadratic: left panel draws elliptical level sets and the step-by-step path using A-conjugate search directions (contrasted with a preconditioned variant). Right panel tracks residual norms ||r_k|| and a meter for the A-conjugacy condition p_k^T A p_{k-1}≈0, illustrating independent 1-D minimizations over expanding Krylov subspaces.

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t=0s

practical uses

01.Solving large sparse SPD linear systems from PDEs (Poisson, diffusion, FEM stiffness matrices)
02.Least-squares and ridge-regularized problems via normal equations (when appropriate)
03.Training/solving quadratic models and using preconditioners to accelerate iterative solvers in scientific computing

technical notes

Implements a fixed 2D SPD quadratic (A,b) and precomputes a few CG/PCG iterates. Animation interpolates along the current segment (eased) and alternates highlighting CG vs PCG each half-cycle. Contours are drawn via coarse grid sampling for a retro blocky look; all geometry is snapped to a pixel grid sized from scale.

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