Introduction to Numerical Computations |
Contents
Basic Aspects of Numerical Computations | 3 |
Computer Arithmetic | 20 |
5 | 49 |
Copyright | |
6 other sections not shown
Common terms and phrases
a₁ a₂ accuracy applied approximate solution arithmetic b₁ b₂ bisection method coefficients computed value consider convergence decimal defined denote derived determine difference equation differential equation digits discussed efficiency error analysis error bound error estimate Euler's method evaluate exact solution example Exercise fact floating point numbers function f(x Gauss-Seidel method Gaussian elimination given gives Hence ill-conditioned Input interpolation interval iterative methods Jacobi method least squares approximation matrix multiplications Newton's method nonzero normal equations obtain operations Output partial pivoting permutation matrix perturbation polynomial of degree rational function recursion reduction relative error result right-hand side roots rounding error Runge-Kutta Runge-Kutta method satisfies secant secant method Section spline starting values step subtractive cancellation Table theorem tion truncation error unstable upper triangular write x₁ xx+1 y(xx y₁ Yk+1 zero