Scientific Computing: An Introductory Survey

accuracy algorithm approximate solution backward error basis functions boundary conditions boundary value problem column component computational problem condition number conjugate gradient method convergence rate data points denoted derivative determine diagonal differential equations digits dimensions discrete eigenvalues eigenvectors entries Euler's method evaluated example finite difference floating-point arithmetic floating-point number floating-point system formula function f Gaussian elimination given golden section search grid implementation input integral interval iterative methods least squares problem library routine linear least squares linear system MATLAB matrix mesh method for solving minimum multiple netlib Newton's method nonlinear equations nonsingular nonzero numerical analysis numerical methods obtain optimization orthogonal parameter PDEs pivoting plot polynomial interpolation positive definite quadratic quadrature rule random numbers relative error root rounding error scientific computing Section sequence stability stepsize symmetric tion transformation True or false underflow upper triangular variables vector xk+1 y₁ zero