Scott, D. S. | Search NASA

NASA NTRS1978

The Lanczos algorithm with selective orthogonalization

A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al.

Parlett, B. N.↗

NASA NTRS1976

Non-dimensional groups in the description of finite-amplitude sound propagation through aerosols

Several parameters, which have fairly transparent physical interpretations, appear in the analytic description of finite-amplitude sound propagation through aerosols. Typically, each of these parameters characterizes, in some sense, either the sound or the aerosol. It also turns out that fairly obvious combinations of these parameters yield non-dimensional groups which, in turn, characterize the nature of the acoustic-aerosol interaction. This theme is developed in order to illustrate how a quick examination of such parameters and groups can yield information about the nature of the processes involved, without the necessity of extensive mathematical analysis. This concept is developed primarily from the viewpoint of sound propagation through aerosols, although complimentary acoustic-aerosol interaction phenomena are briefly noted.

Scott, D. S.↗