The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of "Cascading Accumulators" is the fastest of several methods. The Double Compensation method (in both single and double precision versions) is also… (More)
Development Administration for their assistance and comments. NASDA is also grateful for the contributions of the members of its Research Division who participated in focus group discussions that helped shape the issues and who provided valuable input on the report. We also acknowledge the many incentive program managers who took the time to respond to our… (More)
A set of subroutines is described for combining pmrs of sparse matrices in special cases m which one of the matrices may be regarded as full, and/or a vector, and/or an elementary matrLx. Tests show that in many cases the new routines are faster than an earlier set of more general-purpose routines. Also, a new (faster) routine is given for multiplying two… (More)
Newton's method for solving polynomial equations converges only linearly to a multiple root. The speed of several methods for accelerating the convergence have been compared numerically. The Madsen-Reid method proved to be the fastest, with the Aitken and Ostrowsky methods close behind.
DESCRIPTION Eight FORTRAN subroutines are presented for multiplying and adding pairs of sparse matrices in special cases, that is, in which one of the pair is full and/or a vector or an elementary matrix. Also, a new subroutine for multiplication of two sparse matrices is presented. A detailed description of the individual subroutines and input thereto is… (More)