We present a better algorithm for path planning on complex terrain in the presence of observers and define several metrics related to path planning to evaluate the quality of various terrain compression strategies.

In this paper, we propose a new algorithm for computing a singular value decomposition of a product of three matrices. We show that our algorithm is numerically desirable in that all relevant residual elements will be numerically small In diesem Beitrag wird ein neuer Algorithmus zur Berechnung der Singulärwertzerlegung des Produktes dreier Matrizen vorgestellt. Es wird gezeigt, daβ der Algorithmus ein gutartiges numerisches Verhalten aufweist, weil alle relevanten Residualgröβen klein werden. Nous proposons dans cet article un nouvel algorithme de calcul de la décomposition en valeurs singulières d'un produit de trois matrices. Nous montrons que notre algorithme est attrayant du point de vue numérique du fait que tous les résidus pertinents sont numériquement petits.

We present a new algorithm and systolic array for adaptive beamforming. Our approach improves on McWhirter's pioneering work in two respects. First, our algorithm uses only orthogonal transformations and thus should have better numerical properties. Second, the algorithm can be implemented on one single p × p triangular array of programmable processors that offers a throughput of one residual element per cycle.

Consideration is given to the computation of the singular value decomposition (SVD) on the Connection Machine (CM). Brief descriptions of the Lisp language and some typical matrix manipulating functions are given. Implementation details of various Jacobi-SVD algorithms on an 8192-processor CM are presented. For n*n matrices, where n>

The authors present novel fault-tolerance schemes for 2-D systolic implementation of a recursive least squares minimization problem with applications to beamforming problems. They show that the errors can be detected by examining only a few scalars. In the case of the transient errors the technique is self-correcting. The technique can be implemented with negligible algorithm modification and little additional hardware. The simplicity of the method invites its use in future systolic arrays.>

The authors consider two parallel Jacobi algorithms, due to R.P. Brent et al. (J. VLSI Comput. Syst., vol.1, p.242-70, 1985) and F.T. Luk (1986 J. Lin. Alg. Applic., vol.77, p.259-73), for computing the singular value decomposition of an n*n matrix. By relating the algorithms to the cyclic-by-rows Jacobi method, they prove convergence of the former for odd n and of the latter for any n. The authors also give a nonconvergence example for the former method for all even n>or=4.>

The Coordinate Rotation Digital Computer (CORDIC) algorithms provide a VLSI hardware technique for computing the inverse tangents and vector rotations needed by many matrix decomposition algorithms. A novel simplified CORDIC processor composed of floating-point data paths with a fixed-point angle calculation is proposed. This hybrid processor possesses sufficient accuracy for matrix computations such as the QRD, eigenvalue decomposition, and the singular value decomposition. The simplified structure allows for efficient VLSI implementation.>

Arithmetic issues in the calculation of the Singular Value Decomposition (SVD) are discussed. Traditional algorithms using hardware division and square root are replaced with the special-purpose CORDIC algorithms for computing vector rotations and inverse tangents. The CORDIC 2 × 2 SVD processor can be twice as fast as one assembled from traditional hardware units. A CORDIC SVD processor array is suitable for VLSI implementation and is important for use in real-time signal processing applications.

We introduce a unified checksum scheme for the LU decomposition, Gaussian elimination with pairwise pivoting, and the QR decomposition. The purpose is to detect and locate a transient error during a systolic array computation. We show how to represent the error as a rank-one perturbation to the original data, so that we need not worry when the error occurred. Finally, we perform a floating point error analysis to determine the effects of rounding errors on the checksum scheme.

A linear algebraic interpretation is developed for previously proposed algorithm-based fault tolerance schemes. The concepts of distance, code space, and the definitions of detection and correction in the vector space R/sup n/ are explained. The number of errors that can be detected or corrected for a distance-(d+1) code is derived. It is shown why the correction scheme does not work for general weight vectors, and a novel fast-correction algorithm for a weighted distance-5 code is derived.>

Examines the checksum methods of Abraham et al. for LU decomposition on multiprocessor arrays. Their methods are efficient for detecting a transient error, but expensive for correcting it due to the need for a computation rollback. The authors show how to avoid the rollback by using matrix updating techniques, and they introduce new checksum methods for Gaussian elimination with pairwise pivoting and for QR decomposition on systolic arrays.>

Arithmetic issues in the calculation of the Singular Value Decomposition (SVD) are discussed. Traditional algorithms using hardware division and square root are replaced with the special purpose CORDIC algorithms for computing vector rotations and inverse tangents. The CORDIC 2×2 SVD processor can be twice as fast as one assembled from traditional hardware units. A prototype VLSI implementation of a CORDIC SVD processor array is planned for use in real-time signal processing applications.

We describe a new parallel algorithm for computing the generalized singular value decomposition of two n × n matrices, one of which is nonsingular. Our procedure requires O (n) time and one triangular array of O(n2) processors.

We present a block Lanczos method for computing the greatest singular values and associated vectors of a large and sparse matrix, say A. Our algorithm does not transform A but accesses it through a user-supplied routine that computes the product AX or A tX for a given matrix X.This paper includes a discussion of the various ways to compute the singular-value decomposition of an upper triangular band matrix, this problem arises as a subproblem to be solved in the block Lanczos procedure.

This paper presents the computation of the singular-value decomposition of a matrix on the ILLIAC IV computer.The architecture of the machme is described and it is explained why the standard Golub-Remsch algorithm is not apphcable to this problem.Then a one-sided orthogonalization method is presented.This method makes very efficmnt use of the parallel-computing abilities of the [LLIAC machine The method is shown to be Jacobi-hke and numerically stable.Finally, a comparison of the method on the ILLIAC IV computer with the Golub-Reinsch algorithm on a conventional machme demonstrates the great potentml of parallel computers m the important area of matrLx computations Key Words and Phrases ILLIAC IV computer, singular-value decomposmon, Golub-Remsch algorithm, Jacobl-hke method, parallel matrix computations CR Categories 5 14