A simple approach is described for the error analysis of division-free algorithms. Applications to the comparison of algorithms for extended sums, products, real polynomial evaluation, complex polynomial evaluation are also given.

The error complexity analysis of three algorithms for matrix multiplication and matrix chain product has been given. It is shown that the usual inner product type algorithm is by far the best algorithm for simple matrix multiplication or matrix chain product in terms of minimal basic term growth and minimal error complexities, the latter being independent of the order of pairwise matrix multiplications. Winograd's algorithm is comparable to the usual one, although in matrix chain product the error and data complexities are very sensitive to the order of pairwise matrix multiplication. Strassen's algorithm is not very attractive numerically for having the largest upper bound for both the maximum error complexity and the number of basic terms generated.

An efficient algorithm for storing and constructing a Neville-type divided difference table for general Hermite interpolatmn is described.This table contains all the information needed for multipoint interpolation where for better accuracy a new interpolation polynomial is desired such that for each given point ~ the interpolating points x,(z = 0, 1, . . ., n) are reordered to cluster around 5. Key Words and Phrases" polynomial, multipoint interpolation,

Efficiently computable a posteriori error bounds are attained by using a posteriori models for bounding roundoff errors in the basic floating-point operations. Forward error bounds are found for inner product and polynomial evaluations. An analysis of the Crout algorithm in solving systems of linear algebraic equations leads to sharper backward a posteriori bounds. The results in the analysis of the iterative refinement give bounds useful in estimating the rate of convergence. Some numerical experiments are included.