Numerical Analysis I, Fall 2017 (http://www.math.nthu.edu.tw/˜ wangwc/)

Preparation guide for Quiz 03

The exam problems will be closely related to your homework problems. Make sure you understand all of them.

1. Section 3.1: Learn how to construct Lagrange interpolating polynomials and practice on implementing it. Direct evaluation will do, but Neville’s method is encouraged (extra credit).

2. Section 3.1: Study the error formula (identity) for Lagrange interpolation and how to obtain an error bound (inequality).

3. Section 3.2: Study how to obtain P_{0,1,···,k} from P_{0,1,···,j−1,j+1,···,k} and P_{0,1,···,i−1,i+1,···,k}.

4. Section 3.2: Study how to solve nonlinear equations with Inverse Interpolation.

5. Section 3.5: Study the meaning of cubic spline and how to match the coefficients at x_{j} (such as problems 12, 13, 14). Memorize the meaning of natural and clamped boundary conditions.

6. Section 3.5: Study how to obtain the degree of the piecewise polynomial and number of boundary condition needed for a C^{k} spline.