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PREPARATION FOR COMPUTING
chapter APPROXIMATION OF ROOTS OF fx 0
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absolute error accuracy accurate Algebra Algorithm 12.5 approximate solution approximate the solution assume augmented matrix bisection method boundary value problem calculator Chapter coefficients column Compare complex roots compute convergence decimal places derivative determine diagonal difference equation digits discretization error eigenvalues equation x3 error bound error estimate error term Euler exact solution EXAMPLE Exercise Set formula function Gauss algorithm given Householder transformation initial estimates initial-value problem input integral interpolation polynomial interval linear system machine output machine program machine results mathematics Newton algorithm Newton's method numerical analysis numerical methods numerical results numerical solution obtained partial differential equation points x0 polynomial equation polynomial of degree procedure produce QR algorithm quadratic real roots Repeat exercise root estimate round-off error Runge-Kutta method sequence Simpson Solve the system STAGE NUMBER step size h Suppose table of values Theorem total error truncation error vector Verify x„+i zero