The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Fast Numerical and Machine Learning Algorithms for Spatial Audio Reproduction

Audio reproduction technologies have underwent several revolutions from a purely mechanical, to electromagnetic, and into a digital process. These changes have resulted in steady improvements in the objective qualities of sound capture/playback on increasingly portable devices. However, most mobile playback devices remove important spatial-directional components of externalized sound which are natural to the subjective experience of human hearing. Fortunately, the missing spatial-directional parts can be integrated back into audio through a combination of computational methods and physical knowledge of how sound scatters off of the listener's anthropometry in the sound-field. The former employs signal processing techniques for rendering the sound-field. The latter employs approximations of the sound-field through the measurement of so-called Head-Related Impulse Responses/Transfer Functions (HRIRs/HRTFs). This dissertation develops several numerical and machine learning algorithms for accelerating and personalizing spatial audio reproduction in light of available mobile computing power. First, spatial audio synthesis between a sound-source and sound-field requires fast convolution algorithms between the audio-stream and the HRIRs. We introduce a novel sparse decomposition algorithm for HRIRs based on non-negative matrix factorization that allows for faster time-domain convolution than frequency-domain fast-Fourier-transform variants. Second, the full sound-field over the spherical coordinate domain must be efficiently approximated from a finite collection of HRTFs. We develop a joint spatial-frequency covariance model for Gaussian process regression (GPR) and sparse-GPR methods that supports the fast interpolation and data fusion of HRTFs across multiple data-sets. Third, the direct measurement of HRTFs requires specialized equipment that is unsuited for widespread acquisition. We ``bootstrap'' the human ability to localize sound in listening tests with Gaussian process active-learning techniques over graphical user interfaces that allows the listener to infer his/her own HRTFs. Experiments are conducted on publicly available HRTF datasets and human listeners

Remarks on the optimal convolution kernel for CSOR waveform relaxation

The convolution SOR waveform relaxation method is a numerical method for solving large-scale systems of ordinary differential equations on parallel computers. It is similar in spirit to the SOR acceleration method for solving linear systems of algebraic equations, but replaces the multiplication with an overrelaxation parameter by a convolution with a time-dependent overrelaxation function. Its convergence depends strongly on the particular choice of this function. In this paper, an analytic expression is presented for the optimal continuous-time convolution kernel and its relation to the optimal kernel for the discrete-time iteration is derived. We investigate whether this analytic expression can be used in actual computations. Also, the validity of the formulae that are currently used to determine the optimal continuous-time and discrete-time kernels is extended towards a larger class of ODE systems.status: publishe