Arithmetically improved algorithmic performance

An augmented set of floating-point arithmetic operations which includes the accurate inner product can be routinely employed with benefit in some standard iterative numerical algorithms. Benefits include the requirement of fewer iterations for achieving computational convergence criteria and more accurate results for a given number of iterations. Not all algorithms are benefited, but favorable results have been obtained for the QR algorithm, the conjugate gradient algorithm and the separating hyperplane algorithm. © 1985 Springer-Verlag.