Successive approximation

Trapezoid Rule and Simpson’s Rule Trapezoid Rule y h h h x b

because these edges belong to two successive area-elements, one on the left and the other on the right. This explains the form of the Simpson’s Rule approximation which we now state De nition: Let nbe even. The n-subinterval Simpson approximation to R b a f(x) dxis given by S n = h 3 (y 0 + 4y 1 + 2y 2 + 4y 3 + 2y 4 + + 2y n 2 + 4y n 1 + y n ...

  Approximation, Successive

A Simple Explanation of Partial Least Squares

approximation of X via T jk:= XP jk; where T jk can be understood as a n kcompression of the n mmatrix that captures most of the variance of the data in X. The idea behind principal component regression is to use T jk, for a suitable value of k, in place of X as the design matrix. By construction, the columns of T jk are uncorrelated. 4

  Tesla, Square, Partial, Approximation, Partial least squares

ODE and PDE Stability Analysis

Stability of ODE vs Stability of Method • Stability of ODE solution: Perturbations of solution do not diverge away over time • Stability of a method: – Stable if small perturbations do not cause the solution to diverge from each other without bound – Equivalently: Requires that solution at any fixed time t remain bounded as h → 0 (i.e., # steps to get to t grows)