Numerical Analysis

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13 domain-specific abstractions whose origin domain is Numerical Analysis.

• Aitken's delta-squared process — A nonlinear sequence transformation that accelerates approximately linear convergence by extrapolating from three consecutive terms and canceling the leading error mode.
• Boole's rule — A closed Newton–Cotes quadrature rule using five equally spaced samples to approximate an integral by a weighted quartic interpolant.
• Error analysis (mathematics) — The study of how approximation, rounding, truncation, measurement, discretization, and conditioning create and propagate uncertainty in mathematical results.
• Euler Method — An explicit first-order ODE integrator that advances an initial state by adding the step size times the derivative evaluated at the current numerical state.
• FETI-DP — A dual–primal nonoverlapping domain-decomposition solver that assembles selected interface degrees of freedom globally while enforcing continuity of the remaining duplicated interface variables with Lagrange multipliers.
• Finite difference — The difference between function values at finitely separated arguments, used as a discrete operator and as an approximation to derivatives.
• Halton sequence — A deterministic low-discrepancy sequence in the unit cube formed by combining one-dimensional radical-inverse sequences in pairwise coprime bases.
• Iterative method — A numerical procedure that repeatedly updates an approximation from prior iterates toward a solution under a convergence rule.
• Neumann–Dirichlet method — A nonoverlapping domain-decomposition preconditioner that alternates Neumann and Dirichlet subdomain solves across shared interfaces.
• Residual (numerical analysis) — The discrepancy obtained by substituting an approximate solution into the original equation, usually b−f(x₀) or its signed convention.
• Spectral Element Method — A high-order PDE discretization that partitions a domain into elements and represents each element with high-degree polynomial bases, combining finite-element geometry with spectral accuracy.
• Spectral method — Approximate a differential-equation solution on a usually single global domain by a truncated expansion in smooth global basis functions, then determine its coefficients through Galerkin, tau, collocation, or related residual conditions with convergence tied to regularity and basis fit.
• Truncation error — The discrepancy introduced when an exact infinite, limiting or continuous mathematical process is replaced by a finite approximation, distinct from finite-precision roundoff and analyzable through omitted terms or local discretization expansions.