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01 ·Numerical Computing·★ MEMBER·13 min read Solving Systems of Equations — Direct Methods and Iterative Methods How much a bridge sags, how heat spreads through a room, what a Gaussian process predicts — once a computer gets hold of them they all turn into the same shape, Ax = b. This article builds up elimination (LU) and approximation (conjugate gradients) from zero, through why a million-unknown system can't be solved by elimination, all the way to condition numbers, preconditioning, and matrix-free solvers.