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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Polynomial interpolation
Distinct nodes determine a unique polynomial of bounded degree passing through their data.
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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.
LU factorization
With appropriate pivoting, triangular factors reduce linear-system solution to substitution.
Splines
Piecewise polynomials joined with specified smoothness approximate data and curves.
Bisection method
Continuity and opposite endpoint signs allow repeated halving to bracket a root.
Knowledge connections
- Splines · Related · Map context
- Finite differences · Related · Map context
- Floating-point arithmetic · Related · Map context
- LU factorization · Related · Map context