compendia types: Published Papers(130) Journal or Magazine Articles(44) Working Papers(1) Problem Sets(1) Books(1)

research fields: Computer and Information Sciences(175) Statistics(2) Econometrics(2)

1 through 25 of 163 resultsF1000Research

Daniel A. Beard, Klas H. Pettersen, Brian E. Carlson, Stig W. Omholt, Scott M. Bugenhagen

The asserted dominant role of the kidneys in the chronic regulation of blood pressure and in the etiology of hypertension has been debated since the 1970s. At the center of the theory is the observation that the acute relationships between arterial pressure and urine production—the acute pressure-diuresis and pressure-natriuresis curves—physiologically adapt to perturbations in pressure and/or changes in the rate of salt and volume intake. These adaptations, modulated by various interacting neurohumoral mechanisms, result in chronic relationships between water and salt excretion and pressure that are much steeper than the acute relationships. While the view that renal function is the ...

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Timothy A. Davis

An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations. The simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to ...

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Patrick R. Amestoy, Enseeiht-Irit, Timothy A. Davis, Iain S. Duff

AMD is a set of routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. There are versions written in both C and Fortran 77. A MATLAB interface is included.

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Robert C. Kirby

Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques.

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Valérie Frayssé, Luc Giraud, Serge Gratton, Julien Langou

In this article we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and efficiency the GMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning and the dot product computations. For distributed memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, which is a well-known bottleneck of efficiency for the Krylov methods. Either implicit or explicit calculation of ...

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Tobin A. Driscoll

The Schwarz--Christoffel Toolbox (SC Toolbox) for MATLAB, first released in 1994, made possible the interactive creation and visualization of conformal maps to regions bounded by polygons. The most recent release supports new features, including an object-oriented command-line interface model, new algorithms for multiply elongated and multiple-sheeted regions, and a module for solving Laplace's equation on a polygon with Dirichlet and homogeneous Neumann conditions. Brief examples are given to demonstrate the new capabilities.

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Michael W. Berry, Shakhina A. Pulatova, G. W. Stewart

In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi--Gram-Schmidt--algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form (XR11−1)(R11 R12), where X consists of columns of A. The second, the SCR approximation, is of the form the form A ≅ ...

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James H. Money, Qiang Ye

eigifp is a MATLAB program for computing a few extreme eigenvalues and eigenvectors of the large symmetric generalized eigenvalue problem Ax = λ Bx. It is a black-box implementation of an inverse free preconditioned Krylov subspace projection method developed by Golub and Ye [2002]. It has important features that allow it to solve some difficult problems without any input from users. It is particularly suitable for problems where preconditioning by the standard shift-and-invert transformation is not feasible.

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Tangan Gao, T. Y. Li, Mengnien Wu

MixedVol is a C++ software package that computes the mixed volume of n finite subsets of ℤn or the support of a system of n polynomials in n variables. The software produces the mixed volume as well as the mixed cells. The mixed cells are crucial for solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes for mixed-volume computation in speed by a substantial margin and its memory requirement is very low.

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Andreas Klimke, Barbara Wohlmuth

To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic factor. We describe three possible piecewise multilinear hierarchical interpolation schemes in detail and conduct a numerical comparison. Furthermore, we document the features of our sparse grid interpolation software package spinterp for MATLAB.

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Spencer Shellman, K. Sikorski

We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications in economics, game theory, and the solution of partial differential equations. PFix computes an approximation that satisfies the residual error criterion, and can also compute an approximation satisfying the absolute error criterion when the Lipschitz constant is less than 1. For functions defined on all rectangular domains, the worst-case complexity of PFix has order equal to the logarithm of the ...

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Timothy A. Davis

The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 executable lines of code. The package is written in C, and includes a MATLAB interface.

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Amparo Gil, Javier Segura, Nico M. Temme

Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions U(a, x), V(a, x) and their derivatives for real a and x (x ≥ 0). The code also computes scaled functions. The range of computation for scaled PCFs is practically unrestricted. The aimed relative accuracy for scaled functions is better than 5 10−14. Exceptions to this accuracy are the evaluation of the functions near their zeros and the error caused by the evaluation of trigonometric functions of large arguments when |a| ≫ x. The routines always give values for which the Wronskian ...

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William W. Hager, Hongchao Zhang

Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition gTkdk ≤ −7/8 ‖gk‖2 and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.

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Laurent Granvilliers, Frédéric Benhamou

RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or nonsquare, sparse or dense, linear, polynomial, or involving transcendental functions.The modeling language permits stating constraint models and tuning parameters of solving algorithms which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, and 3B) are implemented. The distribution includes C sources, executables for different machine architectures, ...

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Leslie Foster, Rajesh Kommu

Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require O(mn2) operations to solve min ‖b − Ax‖ where A is an m by n matrix. We present a modification of the LAPACK routine xGELSY that requires O(mnk) operations where k is the effective numerical rank of the matrix A. For low rank matrices the modification is an order of magnitude faster than the LAPACK code.

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Peter Benner, Daniel Kressner

This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.

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Fayez A. Alhargan

A continued fraction function algorithm is developed to evaluate general-order Mathieu characteristic numbers, and a new technique is presented for evaluating the Mathieu determinant which can be used to compute the order directly. Approximate expressions are developed to estimate the orders and Mathieu characteristic numbers for the root, finding algorithms. The algorithms, with minor modifications, were used for computing Mathieu coefficients of general order. The algorithms can deal with a large range of Mathieu characteristic number c, real and complex order ν, and parameter h.

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Genetha A. Gray, Tamara G. Kolda

APPSPACK is software for solving unconstrained and bound-constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed via a separate program or script; the code can be run serially or in parallel, regardless of whether the function evaluation itself is parallel; and the software is freely available. We describe the underlying algorithm, data structures, and features of APPSPACK version 4.0, as well as ...

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Hai-Jun Su, J. Michael McCarthy, Masha Sosonkina, Layne T. Watson

Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked and handling singular solutions have made probability-one homotopy methods even more practical. POLSYS_GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm ...

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Joris Van Deun, Ronald Cools

We present an algorithm to compute integrals of the form ∫∞0 xm ∏ki = 1Jνi(aix)dx with Jνi(x) the Bessel function of the first kind and (real) order νi. The parameter m is a real number such that ∑i νi + m > −1 and the coefficients ai are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for Jνi(x) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Γ(a,z). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.

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Pierluigi Amodio, Giuseppe Romanazzi

BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with bordered almost block diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is, having a block upper bidiagonal structure with an additional block in the right upper corner. The algorithm implemented in the package performs cyclic reduction of the coefficient matrix in order to reduce the fill-in due to the corner block.

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Eduardo N. Gonçalves, Reinaldo M. Palhares, Ricardo H. C. Takahashi, Renato C. Mesquita

This article presents a simple efficient algorithm for the subdivision of a d-dimensional simplex in kd simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of kd subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.

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Danilo Erricolo

A translation to Fortran 90 of Gertrude Blanch's algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented.

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Brett W. Bader, Tamara G. Kolda

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor_as_matrix class supports the “matricization” of a tensor, that is, the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp_tensor and tucker_tensor. We describe all of ...

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