Runge-Kutta method improves Euler by providing higher-order accuracy with k₁,k₂,k₃,k₄

Finite element method

Runge-Kutta method improves Euler by providing higher-order accuracy with k₁,k₂,k₃,k₄

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

second-order methods (Newton's) converge faster but are expensive: O(n³) per step

Second-order methods converge faster due to quadratic convergence but are expensive due to O(n³) per iteration

Euler method

Euler method approximates ODE solution with y_{n+1} = y_n + h·f(y_n)

iterative methods (CG, GMRES) do: solve Ax=b without explicitly inverting A

Iterative methods solve Ax=b without explicitly inverting A

quantization to INT8 doubles throughput

Quantization to INT8 doubles throughput because tensor cores process INT8 2x faster

Ordinary least squares

OLS minimizes squared differences

approximation algorithms guarantee: solution within factor α of optimal

Can we always find the best solution quickly?

Swipe through 100 ML concepts daily