Some general principles of numerical calculation; How to obtain and estimate accuracy in numerical calculations; Numerical uses of series; Approximation of functions; Numerical linear algebra; Nonlinear equations; Finite difference with applications to numerical integrations, differentation, and interpolation; Differential equations; Fourier methods; Optimization; The Monte Carlo method and application; Solutions to problems.
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HOW TO OBTAIN AND ESTIMATE ACCURACY
NUMERICAL USES OF SERIES
APPROXIMATION OF FUNCTIONS
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accuracy algorithm analysis applications assume band matrix boundary conditions calculation coefficients column computed condition number convergence curve defined denote derivatives determined diagonal difference equation differential equation digits eigenvalues eigenvectors elements equal equidistant error bound error estimate Euler's method Example expansion Fourier function Gaussian elimination given gives Hence ill-conditioned input data interval inverse iterative method least-squares linear system linearly independent magnitude mathematical matrix maximum norm Newton-Raphson's method nonlinear notation numerical methods obtained operations orthogonal polynomials perturbations pivoting polynomial of degree positive-definite proof quadratic recursion formula relative error remainder term result Richardson extrapolation right-hand side right-hand variables Romberg's method root round-off errors rounding errors satisfies secant method sequence Show solve spline step length symmetric symmetric matrix system of equations Tchebycheff Theorem tion transformation trapezoidal rule triangular truncation error values zero