Methods of Numerical Integration

a₁ abscissas abscissas and weights accuracy algorithm analysis analytic functions applied approximate integration asymptotic automatic integration bounded CACM Cauchy principal value coefficients Comp computed constant convergence defined derivatives differential equation dimensions dx dy dx₁ error estimate Exact value example expansion finite fo f(x Fourier Transform function f functional evaluations Gauss rule Gaussian given h₁ Hence hypercube indefinite integral infinite integrand integration formula integration rules interpolation interpolatory interval Krylov Laguerre Laplace transform linear Lobatto Lyness Math method monomials multiple integrals Newton-Cotes norm number of functional number of points numerical integration obtain orthogonal polynomials Peano's theorem quadrature formulas Rabinowitz References Riemann Romberg Romberg integration Section sequence Simpson's rule singularity spline Stroud and Secrest subinterval theorem tion trapezoidal rule Tschebyscheff variable w₁ weight function x₁ zeros