## Nevilles Method

Newton's method of interpolation involves two steps computation of the coefficients, followed by evaluation of the polynomial. This works well if the interpolation is carried out repeatedly at different values of x using the same polynomial. If only one point is to be interpolated, a method that computes the interpolant in a single step, such as Neville's algorithm, is a better choice. Let Pk x, xi 1, , xi k denote the polynomial of degree k that passes through the k 1 data points x,, yi , xi...

## Tridiagonal Coefficient Matrix

Consider the solution of Ax b by Doolittle's decomposition, where A is the n x n tridiagonal matrix As the notation implies, we are storing the nonzero elements of A in the vectors The resulting saving of storage can be significant. For example, a 100 x 100 tridiagonal matrix, containing 10,000 elements, can be stored in only 99 100 99 298 locations, which represents a compression ratio of about 33 1. Let us now apply LU decomposition to the coefficient matrix. We reduce row k by getting rid of...