Numerical Analysis and Scientific Computing
Explore errors and equation solving; approximation and quadrature; linear systems and differential equations. Concepts and connections are available independently of video coverage.
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Iterative linear solvers
Repeated approximations solve large linear systems when the iteration satisfies convergence conditions.
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Euler method
Euler's method advances an ODE solution using its current derivative and a step size.
LU factorization
With appropriate pivoting, triangular factors reduce linear-system solution to substitution.
Bisection method
Continuity and opposite endpoint signs allow repeated halving to bracket a root.
Conditioning
Conditioning measures sensitivity of a problem's exact solution to perturbations in its data.
Finite differences
Differences of nearby samples approximate derivatives, balancing truncation and roundoff errors.
Knowledge connections
- LU factorization · Related · Map context
- Euler method · Related · Map context