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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Numerical stability
A stable algorithm controls amplification of rounding and data errors relative to the problem.
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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.
Euler method
Euler's method advances an ODE solution using its current derivative and a step size.
Finite differences
Differences of nearby samples approximate derivatives, balancing truncation and roundoff errors.
Floating-point arithmetic
Finite-precision arithmetic introduces rounding and has bounded representable ranges.
Knowledge connections
- Conditioning · Related · Map context
- Bisection method · Related · Map context
- Conditioning · Prerequisite · Map context