Abstract. The evolution of digital libraries and the Internet has dramatically transformed the processing, storage, and retrieval of information. Efforts to digitize text, images, video, and audio now consume a substantial portion of both academic and industrial activity. Even when there is no shortage of textual materials on a particular topic, procedures for indexing or extracting the knowledge or conceptual information contained in them can be lacking. Recently developed information retrieval technologies are based on the concept of a vector space. Data are modeled as a matrix, and a user’s query of the database is represented as a vector. Relevant documents in the database are then identified via simple vector operations. Orthogonal factorizations of the matrix provide mechanisms for handling uncertainty in the database itself. The purpose of this paper is to show how such fundamental mathematical concepts from linear algebra can be used to manage and index large text collections. Key words. information retrieval, linear algebra, QR factorization, singular value decomposition, vector spaces

Solving any inverse problem requires understanding the uncertainties in the data to know what it means to fit the data. We also need methods to incorporate dataindependent prior information to eliminate unreasonable models that fit the data. Both of these issues involve subtle choices that may significantly influence the results of inverse calculations. The specification of prior information is especially controversial. How does one quantify information? What does it mean to know something about a parameter a priori? In this tutorial we discuss Bayesian and frequentist methodologies that can be used to incorporate information into inverse calculations. In particular we show that apparently conservative Bayesian choices, such as representing interval constraints by uniform probabilities (as is commonly done when using genetic algorithms, for example) may lead to artificially small uncertainties. We also describe tools from statistical decision theory that can be used to...

. In this paper, we present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We particularly emphasize Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography. The target architectures for our implementations of such methods are the Cray-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications in which approximate pseudo-inverses of large sparse Jacobian matrices are needed. It is hoped that this research will advance the dev...

this memory is statically allocated, whereas on the Alliant FX/80 it is dynamically allocated as needed. On the Cray-2S/4128, the vector z would be both retrieved from and written to core memory. However, on the Alliant FX/80, z may be fetched and held in the 512 kilobyte cache. Since memory accesses from the cache (fast local memory) can almost twice as fast as those from the larger globally-shared memory, we achieve an overall higher computational rate for multiplication by A

Many important details of potential subsurface reservoirs that we wish to characterize are only indirectly present in the reflected wavefields measured at the Earth’s surface. Therefore, the analysis of seismic data always presents an inversion problem. Instead of analyzing the data trace by trace, we propose an automated procedure that adjusts the parameters of a two-dimensional geological model by minimizing the mismatch between the simulated and measured seismic. This approach differs from standard inversion problems in that the size of the required details of the 2D geological reservoir model is far below the limits of the seismic resolution.

Introduction A major goal of exploration geophysics is to determine the structure of the Earth near the surface from measured seismic data. Ideally, one would like to determine the important material parameters (e.g., density, wave speed(s)) as functions of position. This is difficult for a number of reasons: insufficient understanding of the physics (we do not really know the correct form of the differential equations governing wave motion in the subsurface appropriate for inverting seismic data); the ill-posed nature of multidimensional inverse problems for wave equations (even if we knew the correct form of the equations, the coefficients may not be uniquely determined); the very large size of seismic data sets; and numerous practical difficulties in working with seismic data (inaccurate knowledge of the source, noise in the data, etc.). One approach used with some success is to extract from large seismic data sets more tractable data sets consisting of reflection and/or tr

INTRODUCTION The degree of difficulty associated with inverting seismic traveltime data for wave speed distribution is largely determined by the contrasts present in the propagating medium. If velocity contrasts are small, seismic waves are only weakly refracted and straight ray tomographic algorithms will give adequate results (Dines and Lytle, 1979; Lytle and Dines, 1980). If the velocity contrasts are large, then seismic waves are strongly refracted, implying that nonlinear tomography algorithms are required to invert such data. On the other hand, if the measurement configuration of sources and receivers has a severely limited range of view angles (as is often the case in crosswell geotomography), then the reconstruction will not place enough natural constraints (i.e., those derived from data) on the velocity model. In this situation, it is commonly observed that raw reconstructions (prior to regularization) produce wildly oscillating velocity distributions

Abstract not found