An Introduction to Applied Numerical Analysis |
Contents
CHAPTER | 3 |
CHAPTER 5 NONLINEAR SYSTEMS | 181 |
EIGENVALUE PROBLEMS | 214 |
Copyright | |
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a₁ a₂ accuracy accurate Algorithm 12.5 approximate the solution arithmetic assume augmented matrix b₁ b₂ boundary value problem c₁ c₂ calculator coefficients column Compare compute convergence decimal places derivative determine diagonal difference equation discretization error divided difference eigenvalues error estimate error term Euler exact solution EXAMPLE Exercise Set formula function ƒ Gauss given Householder transformation initial estimates initial-value problem integral interpolation polynomial interval iterations k₁ linear system machine output machine program matrix numerical methods numerical results numerical solution obtained partial differential equation points xo polynomial equation polynomial of degree procedure QR algorithm quadratic real roots Repeat exercise root estimate round-off error Runge-Kutta method S₁ sequence Simpson Solve the system step size h Suppose table of values Taylor polynomial Theorem total error trapezoid tridiagonal tridiagonal matrix truncation error vector Verify x₁ Xn+1 y₁ Yn+1 zero