In this paper we describe the considerations that led us to the design of LDL and nrovide an overview of the features of-this language. L$L is designed to combine the flexibility of logic programming with the high performance of the relational database technology. The design offers an improved mode of control over the existing logic programming languages together with an enriched repertoire of ...

Suppose we are given the conditional proba­ bility of one variable given some other vari­ ables. Normally the full joint distribution over the conditioning variables is required to determine the probability of the conditioned variable. Under what circumstances are the marginal distributions over the conditioning variables sufficient to determine the probabil­ ity of the conditioned variable? Su...

Given a sparse, symmetric positive definite matrix C and an associated sparse Cholesky factorization LDL, we develop sparse techniques for updating the factorization after a symmetric modification of a row and column of C. We show how the modification in the Cholesky factorization associated with this rank-2 modification of C can be computed efficiently using a sparse rank-1 technique developed...

Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient sparse, rank-structured Cholesky algorithm for solution of the positive definite linear system Ax = b when A comes from a discretized partial-differential equat...

We present experiments giving evidence for the onset of irregular spatio-temporal dynamics on picosecond timescales in broad area lasers and characterize the dynamical complexity. In particular, we present single shot streak camera measurements of the nearfield dynamics of a broad area laser with a 100 μm wide active area and successfully apply Karhunen–Loève Decomposition (KLD) directly to the...

This article aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering algorithms for computing it, the numerical stability of the algorithms, and updating and downdating of the factorization. Cholesky factorization with pivoting for semidefinite matrices is also treated.  2009 John Wiley & Sons, Inc. WIREs Co...

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms exi...

The covariance matrix plays an important role in statistical inference, yet modeling a covariance matrix is often a difficult task in practice due to its dimensionality and the non-negative definite constraint. In order to model a covariance matrix effectively, it is typically broken down into components based on modeling considerations or mathematical convenience. Decompositions that have rece...

Background: Dense LDL phenotypes are associated with increased atherogenicity, and are commonly evaluated for the purposes of atherosclerosis research and cardiovascular risk discrimination. Objective: To examine the ability of LDL subclasses, expressed as a ratio of dense-to-buoyant subclass, to predict LDL

We present a Cholesky LR algorithm with Laguerre’s shift for computing the eigenvalues of a positive definite symmetric diagonal-plus-semiseparable matrix. By exploiting the semiseparable structure, each step of the method can be performed in linear time.