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Topic: Sparse grid

	Scientific Visualization on Sparse Grids
		For interpolation on sparse grids, a hierarchy of basis functions is used, where some functions are defined on the entire grid.
		The actual sparse grid is created by removing the points that do not contribute to the the sparse grid interpolation functions from the associated full grid (Figure 2).
		Sparse grids need only a negligible amount of memory compared with their associated full grids as shown in Table 1.
	www.vis.uni-stuttgart.de /ger/research/fields/recent/sparse (729 words)

	NationMaster - Encyclopedia: Sparse grid
		Sparse grids are a numerical technique to represent, integrate or interpolate high dimensional functions.
		For interpolation on sparse grids, a hierarchy of basis functions is used, where some functions are defined on the entire grid.
		The actual sparse grid is created by removing the points that do not contribute to the the sparse grid interpolation functions from the associated full grid (Figure 2).
	www.nationmaster.com /encyclopedia/Sparse-grid (426 words)

	Proximity Grid
		Grids of medium density (20-70%) achieve a useful amount of separation, and allow fairly large object representations with no overlap: see Figure 5.1(b) for an example of a 70% proximity grid.
		A sparse grid is not a very large departure from the corresponding continuous configuration, and a greedy approach is capable of transforming the latter to the former.
		Sparse grids only give a limited amount of separation, but nonetheless can be useful for configurations with complete overlap or clumps of points.
	www.pavis.org /essay/proximity_grid.html (5971 words)

	RLE Sparse Level Sets - a flexible & scalable level set representation
		These advantages are not all shared by the octree [Strain 1999; Frisken 2000], the sparse field method [Whitaker 1998], or the sparse block grid [Bridson 2003] scalable level set representations.
		The format of the RLE sparse level set structure is as follows: Essentially, each row of the level set is considered as a stream of data, and we use a run-length encoding of the row based on its value.
		For each frame of the animation the model is (1) converted to a 600x600x600 RLE sparse level set volume, (2) down-sampled 300x300x300 to reduce aliasing artifacts, and (3) then rendered.
	www.exocortex.org /siggraph/2004-1.html (838 words)

	ANU - Mathematical Sciences Institute (MSI) - Advanced Computation and Modelling Program
		Sparse grids are "low"-dimensional subspaces of this tensor-product space.
		This sparse grid function space has been introduced several times since the 1960s but has made its debut as a computational tool to solve partial differential equations in 1991 by Zenger.
		It has been shown that these sparse grid spaces are flexible enough to deal with problems of up to around d=10 dimensions.
	wwwmaths.anu.edu.au /research.groups/advcomp/projects-sparse-grids.html (696 words)

	Problem D - Grid Points
		Your task is to write a program which selects the grid points to use based on the points to plot and the number of desired grid points.
		The best choice of grid points is one that fulfills the criteria above and where the difference between the number of grid points used and the desired number of grid points (given in the input) is minimized.
		All grid points in a test case should be printed with same number of digits after the decimal point, and at least one of the grid points should not have trailing zeros after the decimal point.
	acm.uva.es /p/v106/10676.html (603 words)

	Distributed Sparse Grid Visualization
		New algorithms that work entirely on sparse grids can create data sets that cannot be handled on uniform grids any more due to their size.
		As interpolation on sparse grids is a complicated and time consuming process, direct volume visualization is unthinkable for bigger data sets until the underlying interpolation is accelerated by some orders of magnitude.
		The visualization of the incoming ray data is performed in a sparse grid visualization toolkit that effectively hides the parallelization technique from the user.
	wwwvis.informatik.uni-stuttgart.de /ger/research/fields/current/sparsedist/sparsedist-eng.html (906 words)

	Sparse Grids for Time Dependent Problems
		Sparse grids can be constructed from tensor products of one dimensional spaces, where specific parts of the space are cut off.
		The sparse grid construction is related to `hyperbolic crosspoints' and other approximation schemes.
		However, in the presence of sparse grids the additional time discretization is not that expensive.
	wissrech.ins.uni-bonn.de /research/projects/zumbusch/fd.html (818 words)

	KDnuggets News 01:17, item 11, Software (Site not responding. Last check: 2007-11-05)
		Sparse grids where developed in the 90ies and are used for solving high-dimensional partial differential equations.
		High-dimensional wavelet functions on sparse grids are applied to solve regularization problems like that of support vector machines but much faster and in a hierarchical basis making the results interpretable.
		In addition, in the talk "Data mining with sparse grids using simplicial basis functions" by Jochen Garcke of the University of Bonn at the KDD (Research Track 5: Classification and Regression) the sparse grid classification method is described.
	www.kdnuggets.com /news/2001/n17/11i.html (228 words)

	SPARSE: Numerical algorithms for Air Quality Modeling
		Sparse grids were introduced by Zenger in the early nineties to reduce the degrees of freedom in finite element calculations.
		Sparse grids can be considered through multivariate extrapolation techniques.
		By error analysis and experimentation, the supposed advantage of sparse grids must be shown.
	homepages.cwi.nl /~gollum/MAS1.1/SPARSE.html (333 words)

	Adjacency Matrices and Graphs :: Sparse Matrices (Mathematics)
		In addition, the symmetry of the numbering about the equator is apparent in the symmetry of the spy plot about the antidiagonal.
		In a two-dimensional model, a triangular grid surrounds a cross section of the wing and flaps.
		In this example, there are 4253 grid points, each of which is connected to between 3 and 9 others, for a total of 28831 nonzeros in the matrix, and a density equal to 0.0016.
	www.mathworks.com /access/helpdesk/help/techdoc/math/f6-10661.html (929 words)

	Sparse Grids
		The sparse grid method is the basis for a large part of the research done in the department.
		In order to hand a helpful tool to the person who has to explain the sparse grid method, it was decided that a tutorial movie should be created using at that time available facilities.
		Its task is to show an easy approach to the sparse grid method in graphic pictures and based on common foundations.
	wwwwissrech.iam.uni-bonn.de /research/projects/gerstner/sparse/sparse.html (229 words)

	Adaptive Sparse Grids - Hegland (ResearchIndex)
		Abstract: Sparse grids, as studied by Zenger and Griebel in the last 10 years have been very successful in the solution of partial di#erential equations, integral equations and classification problems.
		Adaptive sparse grid functions are elements of a function space lattice.
		Such lattices allow the generalisation of sparse grid techniques to the fitting of very high-dimensional functions with categorical and continuous variables.
	citeseer.ist.psu.edu /hegland01adaptive.html (466 words)

	OrderedMulti2DHexagonalGrid (RePast Documentation v. 2.0)
		The first row of cells is 0, 1, 2 such that 0,0 refers to cell 0, and 0,2 refers to cell 2.
		The ring of neighbors with radius one that surrounds cell 4 is composed of 1, 2, 5, 7, 3, and 0.
		The grid wraps as a toriod such that cell -1, 0 refers to cell 2 and cell 0, -1 is cell 6.
	supportweb.cs.bham.ac.uk /docs/java/repast/api/uchicago/src/sim/space/OrderedMulti2DHexagonalGrid.html (644 words)

	About (Sparse Grid Interpolation Toolbox)
		Specify the minimum or maximum sparse grid depth to compute, or specify the minimum and maximum number of function evaluations to use (for the dimension-adaptive sparse grid).
		Last but not least, the Sparse Grid Interpolation toolbox is designed to easily integrate with your models in Matlab as well as external models.
		Algorithm 847: spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB.
	www.ians.uni-stuttgart.de /spinterp/about.html (530 words)

	Loading Data : Introduction
		To have an idea of how much data is required for a complete grid, think of it like a three-dimensional spreadsheet where multiple sheets extend along the Z axis and where each cell on each sheet represents the values for one observation.
		Generally, sparse data occurs when the unique values for an axis are widely distributed along the axis, for example, an air quality survey where an entire section of a test area was not sampled.
		And often, sparse data is not related spatially, for example, a data set where the X, Y, and Z values are height, weight, and age.
	www.asu.edu /sas/sasdoc/sashtml/specv/z0228758.htm (1175 words)

	HNMS
		The atmosphere is simulated with a discrete number of grid points in specific levels, that begin from the ground, and reach the upper atmospheric layers.
		In those models the grid points extended to the whole earth and the equations are integrated in the three dimentional atmosphere (north and south hemisphere).
		The main differences is that LAM are executed in a limited area, their grid is denser, and they are cabable of simulating accurately the small scale disturbances.
	www.hnms.gr /hnms/english/climatology/climatology_html (433 words)

	ccmm97 abstract: Bungartz (Site not responding. Last check: 2007-11-05)
		Concerning the sparse grid finite element discretization of elliptic partial differential equations, the class of problems that can be tackled has been enlarged significantly in the last years.
		In this contribution, we present a symmetric and an asymmetric variant of the d-dimensional higher order finite element method on sparse grids, using the hierarchical polynomial bases for both the approximation and the test spaces or for the approximation space only, resp., with standard piecewise multilinear hierarchical test functions.
		For both algorithms, the storage requirement at a grid point does not depend on the local polynomial degree p, and p and the resulting representations of the basis functions can be handled in an efficient and adaptive way.
	www.mgnet.org /mgnet/conferences/CopperMtn97/bungartz.html (445 words)

	Cleversafe Open Source Community
		The Cleversafe Research Grid is currently inactive as we switch over to a Consortium Grid with resources provided by worldwide Hosting Providers.
		Although we continue to have record downloads and visits, you may have noticed that news from us has been sparse.
		We have been listening to feedback from the community as well as potential partners, and have been working to incorporate changes into our software.
	www.cleversafe.org (170 words)

	Institut für Numerische Simulation
		In this project, we propose to use a sparse grid method for the direct discretization of Schrödinger's equation.
		For different choices of multi-level bases (real space, Fourier space) for the one-particle state, we will implement the resulting dimension-adaptive sparse grid approaches and compare their properties for Schrödinger's equation.
		On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique.
	wissrech.iam.uni-bonn.de /research/projects/SPP1145 (331 words)

	Chapter 10: Grid (Site not responding. Last check: 2007-11-05)
		Grid defines whether the solution will be 2D or 3D, search parameters, grid spacing and extents, and the data columns in the data file representing the X, Y, (Z), and value data.
		If the point being gridded is at the same location as a data point, the distance between the two locations is zero; if this is not specially treated, a division by zero error occurs.
		As the grid is being generated, the status on the solution is displayed in the log window shown in Figure 10.1.
	uncert.mines.edu /uncert/grid/grid.html (6854 words)

	prudsys AG
		The Sparse Grid technology is one of the most promising approaches in Data Mining because it allows the high-quality analysis of huge data volumes.
		The theoretical fundament of the Sparse Grid approach was originally developed in the sixties by Soviet mathematicians; in the nineties the universities of Munich and Bonn had shaped the numerical basis of the Sparse Grid approximation and made the first implementations.
		This idea has lead to the development of Sparse Grid classification which is realized in close cooperation between prudsys and the University of Bonn since the end of the nineties.
	www.prudsys.com /Presse/Pressemeldungen/?0027 (574 words)

	DAM: Seminars for Jan 22 - Jan 26, 2001
		This method can be viewed as an extension of the Sparse Grid Stochastic Collocation method proposed in [Nobile-Tempone-Webster, Technical report #85, MOX, Dipartimento di Matematica, 2006] which consists of a Galerkin approximation in space and a collocation, in probability space, at the zeros of sparse tensor product spaces utilizing either Clenshaw-Curtis or Gaussian interpolants.
		Our previous sparse collocation procedure is very effective for problems whose input data depend on a moderate number of random variables, which "weigh equally" in the solution.
		In particular, for moderately large dimensional problems, the sparse grid approach with a properly chosen anisotropy seems to be very efficient and superior to all examined methods.
	www.cfm.brown.edu /cgi-bin/dam/view_seminars.cgi?Jan-22-Jan-26-2001 (964 words)

	Numerical Quadrature in Finance
		However, for special function classes, such as spaces of functions which have bounded mixed derivatives, Smolyak's construction (also known as sparse grid method) can overcome this curse of dimension to a certain extent.
		Sparse grid quadrature formulas come in various types depending on a one-dimensional basis integration routine.
		The scope of this project is to apply sparse grid quadrature formulas to various problems from finance.
	wwwwissrech.iam.uni-bonn.de /research/projects/gerstner/finance/finance.html (474 words)

	USGS: ISIS coreg Application Documentation
		A sparse grid will be defined across the held image using the parameters ROWS and COLUMNS.
		Conceptually, the sparse grid defined by ROWS and COLUMNS will be laid on top of both images with even spacing between the rows (or columns) and but no row will touch the top or bottom of the image.
		This is done by centering the search chip at the grid intersection for the image to be translated (FROM) and centering the pattern chip at the grid intersection for the held image (MATCH).
	isis.astrogeology.usgs.gov /Application/presentation/Tabbed/coreg/coreg.html (1163 words)

	alphaWorks : Watson Sparse Matrix Package : Overview
		Watson Sparse Matrix Package (WSMP) is a collection of algorithms for efficiently solving large systems of linear equations whose coefficient matrices are sparse.
		A sparse matrix is one that has relatively few non-zero (or "interesting") entries.
		On a wide range of sparse linear systems and hardware platforms, WSMP has been shown to be significantly faster than other similar software.
	www.alphaworks.ibm.com /tech/wsmp (341 words)

	PRB: Decimals Don't Display Properly in Grid
		For the column that is used to display the numeric data, set the Sparse property to false, and enter a valid input mask for the Textbox object.
		When displaying any numeric or currency information in a grid, it is necessary to set two properties of the grid to limit the display to two and only two decimal places.
		A grid is a combination of several different objects including a text box, so it is necessary to apply some kind of an input mask to the grid text box control.
	support.microsoft.com /kb/135333 (422 words)

	Parallel Adaptive Sparse Grids
		The parallelization of adaptively refined grids in one dimension is simple.
		Consider a refined grid, the domain is partitioned into intervals of equal workload.
		We need to store a hierarchicaly nested sequence of adapted grids which includes nodes (= degrees of freedom) and their geometric relationship on the grid and their relation to nodes on different grid levels.
	wwwwissrech.iam.uni-bonn.de /research/projects/zumbusch/sparse.html (996 words)

	Database Tables about Grid Cells (Site not responding. Last check: 2007-11-05)
		The value for ACRES_PER_GRID_CELL is computed as part of producing the output database, by looking up the grid cell size and units in the urbansim_constants table (so that this constant will be correct for grid cells whose dimensions are in various systems of measurement).
		In particular, it contains a complete snapshot of the grid cell data, for all grid cells, for each year for which the output data is requested in the section of the scenario file.
		Information common to all grid cells, such as size, is stored in the urbansim_constants table.
	www.urbansim.org /docs/data/database_tables/gridcell_tables.xml (784 words)

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