Mathematics · Avançado · Nível 4

Numerical analysis

What a computed answer is worth: the condition number of a problem, backward error and what backward stability does and does not promise, the condition number of a matrix and why a small residual is not a small error, and the digits no method can recover; orders of convergence read from the errors, the contraction mapping theorem with its hypotheses and its two bounds, why Newton's method is quadratic at a simple root and linear at a repeated one, and what acceleration assumes; approximation theory from least squares and orthogonal families through the Chebyshev polynomials, the nodes that minimise the interpolation error factor, and the equioscillation theorem that recognises a best uniform approximation; quadrature by degree of exactness, Gauss rules and the bound they meet, Romberg extrapolation and adaptive subdivision; numerical linear algebra by cost, growth factor and conditioning, QR and least squares, the spectral radius that decides an iteration, Krylov methods and preconditioning, and the power method's rate; and the stability theory of solvers for differential equations — consistency and convergence, the stability function and its region, A-stability, stiffness and Dahlquist's two theorems.

Ages 18+ 26 lessons about 9 hours in all

Podes começar já, seja o que for que tenhas feito antes. Não é preciso terminar primeiro nada desta página. Podes fazer uma pausa quando quiseres; o teu progresso é guardado automaticamente.