Introduction to Numerical Analysis |
Contents
Errors in Numerical Computations 1 | 12 |
Polynomial Approximations and Finite Differences | 41 |
Numerical Integration | 59 |
Copyright | |
4 other sections not shown
Common terms and phrases
a₁ augmented matrix b₁ calculated chapter coefficients column converges corrector decimal places defined derivative determine diagonal difference table differential equation digital computer discussed error analysis error term evaluate EXAMPLE Exercises factorial polynomials finite function f(x Gauss-Seidel method Gaussian quadrature given in Equation gives Gregory-Newton polynomial Hence Hermite interpolation hf(xn hx(x initial condition integral interval iteration method k₁ k₂ Legendre Legendre polynomials matrix multiplication Newton-Cotes formulas Numerical Analysis numerical solution O(h³ obtained order method orthogonal orthogonal polynomials P₁(x P₂(x places of accuracy points polynomial of degree Property quadrature formula real root reduced remainder term Repeat Problem replaced result round-off error Runge-Kutta method sequence set of equations Show Simpson's Simpson's rule step synthetic division tabulation Taylor's series Theorem trapezoidal rule truncation error upper bound values variables x₁ Xi+1 Xn+1 y₁ y₂ Yn+1 zero