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Basic Aspects of Numerical Computations
Evaluation of Functions
6 other sections not shown
accuracy accurate applied approximate solution arithmetic assume backsolving 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 exponent fact floating point numbers function/(x Gauss-Seidel method Gaussian elimination given gives Hence ill-conditioned Input integration formula interval iterative methods Jacobi method least squares approximation matrix multiplications Newton's method nonzero norm normal equations number system obtain operations Output partial pivoting permutation matrix perturbation polynomial of degree rational function recursion reduce relative error result right-hand side roots rounding error Runge-Kutta method satisfies secant method Section Simpson's rule spline starting values step subtractive cancellation suppose Table technique theorem tion trapezoidal truncation error unstable upper triangular write xk+l xu x2 y(xk yk+l zero