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Sparse grids are numerical techniques to represent, integrate or interpolate high dimensional functions. They were originally developed by the Russian
Sparse_grid
Methods of calculating definite integrals
which include the Metropolis–Hastings algorithm and Gibbs sampling. Sparse grids were originally developed by Smolyak for the quadrature of high-dimensional
Numerical_integration
Writing paper with a grid
French quadrillé, 'large square', is a common form of graph paper with a sparse grid printed in light blue or gray and right to the edge of the paper. In
Graph_paper
state quantization Lebedev quadrature — uses a grid on a sphere with octahedral symmetry Sparse grid Coopmans approximation Numerical differentiation
List of numerical analysis topics
List_of_numerical_analysis_topics
Methods for numerical approximations
Carlo integration), or, in modestly large dimensions, the method of sparse grids. Numerical analysis is also concerned with computing (in an approximate
Numerical_analysis
Method by which information is represented in the brain
system. Given a potentially large set of input patterns, sparse coding algorithms (e.g. sparse autoencoder) attempt to automatically find a small number
Neural_coding
Speed of convergence of a mathematical sequence
points in a polygon mesh, the single-dimension spacings of an irregular sparse grid, or a characteristic quantum of energy or momentum in a quantum mechanical
Rate_of_convergence
German mathematician
scientific computing, and he helped develop computer algorithms for sparse grids. Griebel was director of the Institute for Numerical Simulation at the
Michael_Griebel
Type of mathematical sequence
Discrepancy theory Markov chain Monte Carlo Quasi-Monte Carlo method Sparse grid Systematic sampling Beck, József (1989). "A two-dimensional van Aardenne-Ehrenfest
Low-discrepancy_sequence
Parameter-free superresolution algorithm
SAMV (iterative sparse asymptotic minimum variance) is a parameter-free superresolution algorithm for the linear inverse problem in spectral estimation
SAMV_(algorithm)
Signal processing technique
Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and
Compressed_sensing
Chinese-American applied mathematician
discontinuous Galerkin methods, including structure preservation and sparse grid methods for kinetic and transport equations". "August prize spotlight:
Yingda_Cheng
3D computer graphics rendering technique
Checkerboard rendering or sparse rendering, also known as checkerboarding for short, is a 3D computer graphics rendering technique, intended primarily
Checkerboard_rendering
Numerical integration method
quadrature formulas or similar methods. Nested rules are also important for sparse grids in multidimensional quadrature, and Clenshaw–Curtis quadrature is a popular
Clenshaw–Curtis_quadrature
Open source software library for working with sparse volumetric data
"DB+Grid", which was abandoned to emphasize its distinction from similarly named, but different, existing sparse data structures like DT-Grid or DB-Grid.
OpenVDB
Data structure used in image rendering
storage space is still required by the sparse field level set method. See for implementation details. The sparse block grid method, introduced by Bridson in
Level_set_(data_structures)
Type of spatial anti-aliasing
large. A sparse regular grid sample pattern is a subset of samples that are chosen from the regular grid sample pattern. As with the regular grid, attribute
Multisample_anti-aliasing
Logographs in shared East Asian written tradition
talkative 龍 ("dragon" in a grid of four) 䲜 the appearance of many kinds of fish used in the chengyu 生活䲜䲜 㸚 (obsolete) sparse and clear only found in historical
CJK_characters
Type of urban planning design
The fused grid is a street network pattern first proposed in 2002 and subsequently applied in Calgary, Alberta (2006) and Stratford, Ontario (2004). It
Fused_grid
German mathematician (born 1940)
scientific achievements is the discovery of how to harness approximation on sparse grids for the efficient solution of elliptic partial differential equations
Christoph_Zenger
Topics referred to by the same term
with each field stored as a separate array Sparse array, with most elements omitted, to store a sparse matrix Variable-length array Associative array
Array
Grid-based word puzzle
A crossword is a word game consisting of a grid of black and white squares with numbers on the corners, into which solvers enter words or phrases ("entries")
Crossword
Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regularization
Structured sparsity regularization
Structured_sparsity_regularization
2018 studio album by Grouper
relative brevity and sparseness of the album … won't see Grid Of Points talked of in the same elevated way as some of her other work". Grid of Points was ranked
Grid_of_Points
Computational method in Bayesian statistics
under certain assumptions (e.g., based on polynomial approximation on sparse grids, which could potentially heavily reduce the simulation times for ABC)
Approximate Bayesian computation
Approximate_Bayesian_computation
Method of solving differential equations
grid unknowns can be particular linear combinations of fine grid unknowns.) Thus, AMG methods become black-box solvers for certain classes of sparse matrices
Multigrid_method
Device that controls current between electrodes
These electrodes are not solid sheets but sparse elements through which electrons can pass, referred to as grids, influencing but not obstructing the flow
Vacuum_tube
Iterative solving method
nonlinear systems. Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential
Relaxation_(iterative_method)
3D reconstruction technique
each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned
Neural_radiance_field
Discrete Fourier transform algorithm
computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity
Fast_Fourier_transform
Number denoting a graph's closeness to a tree
measure of the sparsity of a graph that is at most equal to its treewidth. Because the treewidth of an n × n {\displaystyle n\times n} grid graph is n {\displaystyle
Treewidth
In order to obtain the phase delays for the entire SAR scene from the sparse grid points, two interpolations are implemented in horizontal and vertical
Atmospheric correction for interferometric synthetic aperture radar technique
Atmospheric_correction_for_interferometric_synthetic_aperture_radar_technique
City in Hokkaido, Japan
Hokkaido's cultural, economic, and political center. Originally a plain sparsely inhabited by the indigenous Ainu people, the area contained a few trade
Sapporo
Mathematical optimization problem restricted to integers
program is sparse. In particular, this occurs when the matrix has a block structure, which is the case in many applications. The sparsity of the matrix
Integer_programming
Mathematical optimization algorithm
{\displaystyle \nabla ^{2}u=0} using finite differences on a uniform grid leads to a sparse linear system A x = b {\displaystyle A\mathbf {x} =\mathbf {b} }
Conjugate_gradient_method
Market town in Cumbria, England
civil parish in Cumbria, England. It lies on the A685 and is surrounded by sparsely populated hill country, about 25 miles (40 km) from the nearest larger
Kirkby_Stephen
neighborhood relatively far removed from downtown, at the time populated sparsely and largely by Germans who worked in the nearby limestone quarries. Growth
List of churches in the Diocese of Buffalo
List_of_churches_in_the_Diocese_of_Buffalo
sampling theorem, it is said that the imaging system is performing sparse sampling. Sparse sampling typically occurs as a way of keeping production costs
Deep learning in photoacoustic imaging
Deep_learning_in_photoacoustic_imaging
County in Florida, United States
up roughly one third of Miami-Dade County's inhabited land area, and is sparsely populated, a stark contrast to the densely populated, urban portions of
Miami-Dade_County,_Florida
Surface-approximation method
values at arbitrary points in 3D space of a function defined on a regular grid. The approach involves approximating the function locally by an expression
Tricubic_interpolation
Marshland area near Burscough, in Lancashire, England
on the West Lancashire Coastal Plain. The mere is a vast marsh, around grid reference SD 41 15 that was, until it was drained, the largest body of fresh
Martin_Mere
Numerical solution method of computational electromagnetics
however, this is not necessarily the case. The FDFD method requires solving a sparse linear system, which even for simple problems can be 20,000 by 20,000 elements
Finite-difference frequency-domain method
Finite-difference_frequency-domain_method
Auto racing sanctioning body for North American open wheel racing
incompatible with CART specifications. The IRL's early seasons consisted of sparse schedules and inexperienced teams, with the degradation in quality especially
IndyCar
Analog of the continuous Laplace operator
Laplace operator, defined so that it has meaning on a graph or a discrete grid. For the case of a finite-dimensional graph (having a finite number of edges
Discrete_Laplace_operator
American physicist
Michael J (eds.). "Inferring circuit mechanisms from sparse neural recording and global perturbation in grid cells". eLife. 7 e33503. doi:10.7554/eLife.33503
Ila_Fiete
territories have installed significant solar power capacity into their electrical grids to supplement or provide an alternative to conventional energy sources.
Solar_power_by_country
Suite of algorithms
sequence of vector fields v t , {\displaystyle v_{t},} t=0,1/5,2/5,3/5,4/5,1; bottom row shows the sequence of grids under ϕ t . {\displaystyle \phi _{t}.}
Large deformation diffeomorphic metric mapping
Large_deformation_diffeomorphic_metric_mapping
Historic county of Wales
With a total area of 1,731 km2 (668 sq miles), it was one of the more sparsely populated counties in Great Britain. The Merioneth area remains one of
Merionethshire
Numerical programming library for the Python programming language
Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them
CuPy
Feature descriptor used in computer vision
computed in dense grids at some single scale without orientation alignment, whereas SIFT descriptors are usually computed at sparse, scale-invariant key
Histogram of oriented gradients
Histogram_of_oriented_gradients
Multifaceted crossword puzzle
crosswords, and sometimes two sets of clues are given for a single puzzle grid. Cryptic crossword puzzles come in two main types: the basic cryptic in which
Cryptic_crossword
Open source middleware system for volunteer and grid computing
SCI/0721124. Guinness World Records ranks BOINC as the largest computing grid in the world. BOINC code runs on various operating systems, including Microsoft
Berkeley Open Infrastructure for Network Computing
Berkeley_Open_Infrastructure_for_Network_Computing
Number divisible only by 1 and itself
not possible to arrange n {\displaystyle n} dots into a rectangular grid that is more than one dot wide and more than one dot high. For example, among
Prime_number
Office building in Washington, D.C.
lobby was the main entrance. Additionally, the interiors were initially sparsely decorated, although colorful tapestries were installed in the cafeteria
Robert C. Weaver Federal Building
Robert_C._Weaver_Federal_Building
Comparison of statistical analysis software
grid data. Toeplitz: algorithms for stationary kernels on uniformly spaced data. Semisep.: algorithms for semiseparable covariance matrices. Sparse:
Comparison of Gaussian process software
Comparison_of_Gaussian_process_software
Algorithm to find Euclidean shortest paths
algorithms that search for a Euclidean shortest path between two points on a grid map while allowing the turns in the path to have any angle. The result is
Any-angle_path_planning
Image reconstruction algorithms
reconstruction technique used for computed tomography by Hounsfield. The iterative sparse asymptotic minimum variance algorithm is an iterative, parameter-free superresolution
Iterative_reconstruction
Measurement of population size per unit area or unit volume
environment. Springer. ISBN 3540657800. OCLC 41320143. "Why Mongolia is sparsely populated?". Esther Fleming. SidmartinBio. Human Population. Global Issues
Population_density
Branch of statistics mathematics
focused more on applications and understanding the effects of dense and sparse observations schemes. The term "Functional Data Analysis" was coined by
Functional_data_analysis
Element representing a value on a grid in three dimensional space
computing, a voxel is a representation of a value on a three-dimensional regular grid, akin to the two-dimensional pixel. Voxels are frequently used in the visualization
Voxel
Economic sector in Western Australia
and the presence of two separate large-scale grids and many microgrids to provide power for the sparsely populated state. Western Australia is the source
Energy_in_Western_Australia
Country in Eastern Europe and North Asia
square kilometre (22 inhabitants/mi2), Russia is one of the world's most sparsely populated countries, with the vast majority of its people concentrated
Russia
Class of computational fluid dynamics methods
J.; Hoekstra, A. G. (2008-05-01). "Performance evaluation of a parallel sparse lattice Boltzmann solver". Journal of Computational Physics. 227 (10): 4895–4911
Lattice_Boltzmann_methods
Kind of binary decision diagram
provides an alternative strong normal form, with improved compression of sparse sets. It is based on a reduction rule devised by Shin-ichi Minato in 1993
Zero-suppressed decision diagram
Zero-suppressed_decision_diagram
Vertebrate brain region
cells, whose activity acts as an inertial compass, and conjecturally with grid cells in the neighboring entorhinal cortex. The earliest description of the
Hippocampus
Human settlement in Scotland
Luskentyre (Scottish Gaelic: Losgaintir) is a sparse settlement on the west coast of Harris, in the Outer Hebrides, Scotland. Luskentyre is situated within
Luskentyre
Capital and largest city of Kyrgyzstan
privately built houses, mostly outside the city centre. Streets follow a grid pattern, with most flanked on both sides by narrow irrigation channels, which
Bishkek
Numerical method for solving physical or engineering problems
large, sparse LU decompositions and Cholesky decompositions still work well. For instance, MATLAB's backslash operator (which uses sparse LU, sparse Cholesky
Finite_element_method
American musician and singer-songwriter
record label Yellow Electric. Grouper's work is wide-ranging, incorporating sparse ambient music, tape, field recordings, acoustic guitar, piano, and vocal
Grouper_(musician)
Capital of Alberta, Canada
merger of the Hudson's Bay Company and the North West Company. It remained sparsely populated until the Canadian acquisition of Rupert's Land in 1870, followed
Edmonton
Programming paradigm in which many processes are executed simultaneously
Sparse linear algebra Spectral methods (such as Cooley–Tukey fast Fourier transform) N-body problems (such as Barnes–Hut simulation) Structured grid problems
Parallel_computing
Peninsula in Scotland
side is Applecross Bay and the Inner Sound. The peninsula is mountainous, sparsely populated, and has only two small roads joining the mainland. One of these
Applecross
Endurance auto racing series
events in Europe and North America with dozens of gentleman drivers at the grid to a professional racing series where the world's largest automakers spent
World_Sportscar_Championship
under a BSD License, which computes the sparse matrix of the 1, 2D, and 3D negative Laplacians on a rectangular grid for combinations of Dirichlet, Neumann
Kronecker sum of discrete Laplacians
Kronecker_sum_of_discrete_Laplacians
American musical duo
polish". The album was recorded on a remote, sparsely populated island in the San Juan archipelago, hence 'off-grid'. "Home". Peter Mulvey. Retrieved July 19
Dave_McGraw_&_Mandy_Fer
Island in the lower Florida Keys, United States
Florida Keys in the United States. It is 3 miles (4.8 km) from US 1 and sparsely populated, with only 43 homes. It is only about 1,140 acres (460 hectares)
No_Name_Key
Mapping arbitrary data to fixed-size values
that space into a grid of cells. The table is often an array with two or more indices (called a grid file, grid index, bucket grid, and similar names)
Hash_function
Model-free reinforcement learning algorithm
transitions and rewards without requiring adaptations. For example, in a grid maze, an agent learns to reach an exit worth 10 points. At a junction, Q-learning
Q-learning
Arch bridge in central London
Gardens) pleasure park, opened in around 1661, the land at Vauxhall remained sparsely populated into the 19th century, with the nearest fixed river crossings
Vauxhall_Bridge
Chinese global infrastructure project
construction materials, railway and highway, automobile, real estate, power grid, and iron and steel. Already, some estimates list the Belt and Road Initiative
Belt_and_Road_Initiative
national grid infrastructure downstream. These can take years to remedy in some cases. Where a generating station is large compared to the connected grid capacity
List of hydroelectric power station failures
List_of_hydroelectric_power_station_failures
Wetland in south-east England
Romney Marsh is a sparsely populated wetland area in the counties of Kent and East Sussex in the south-east of England. It covers about 100 square miles
Romney_Marsh
Capital city of New Zealand
Zealand Company, in 1840. Smith's plan included a series of interconnected grid plans, expanding along valleys and lower hill slopes, but without actually
Wellington
Number of stacked spheres in a pyramid
several other counting problems, including counting squares in a square grid and counting acute triangles formed from the vertices of an odd regular polygon
Square_pyramidal_number
Facilities and systems serving society
airports, public transit systems, tunnels, water supply, sewers, electrical grids, and telecommunications (including Internet connectivity and broadband access)
Infrastructure
Capital city of the Isle of Man
St Matthew. Details of the building of the original Grammar School are sparse, but it seems that William Murrey was deeply involved, retaining the use
Douglas,_Isle_of_Man
Parallel computing platform and programming model
library cuSOLVER – CUDA based collection of dense and sparse direct solvers cuSPARSE – CUDA Sparse Matrix library NPP – NVIDIA Performance Primitives library
CUDA
Town in Merseyside, England
of Lord Street. The area was previously known as South Hawes, and was sparsely populated and dominated by dunes. The area became popular with tourists
Southport
Method in approximation theory
method, meaning the nodes (points in the domain) need not lie on a structured grid, and does not require the formation of a mesh. It is often spectrally accurate
Radial basis function interpolation
Radial_basis_function_interpolation
Village in Cornwall, England
The Okehampton to Wadebridge railway line closed in 1966. Due to the sparsely populated area, ticket sales were always low: 4,500 annually in 1928, dropping
Port_Isaac
Geographical region of Russia comprising North Asia
concluded with the annexation of Chukotka in 1778. Siberia is vast and sparsely populated, covering an area of over 13.1 million square kilometres (5,100
Siberia
U.S. national memorial in Washington, D.C.
help. At the time, the District of Columbia outside of Georgetown was sparsely populated so the federal government rented slaves from their owners who
Washington_Monument
Non-metropolitan district in England
the City of Southend-on-Sea. The eastern part of the district is more sparsely populated. The district was formed on 1 April 1974 under the Local Government
Rochford_District
Topic in comparative religion
independent documentation for Kellner's claimed Asian initiations remains sparse and contested in scholarship. Under Aleister Crowley, Thelema integrated
Western esotericism and Eastern religions
Western_esotericism_and_Eastern_religions
Coastal region of California, United States
is mostly uninhabited, while the coast remains relatively isolated and sparsely populated, with between 1,800 and 2,000 year-round residents and relatively
Big_Sur
Country in Southeast Asia and Oceania
Extending the grid is difficult in sparsely populated and island areas, while reliability problems are reported even in places connected to the grid. Indonesia
Indonesia
Upland between England and Scotland
similar access for the public to the north of the border. In addition, a sparse network of public bridleways and footpaths stretches around the area, often
Cheviot_Hills
Technology developed by Microsoft
Microsoft's Pivot, but not in SeaDragon per se. Sparse images are a sub-classification of the DZI file type. A sparse image is normally a number of separate photographs
Deep_Zoom
Machine learning technique useful for dimensionality reduction
close to it in the SOM grid are adjusted towards the input vector. The magnitude of the change decreases with time and with the grid-distance from the BMU
Self-organizing_map
Katowice District in Silesian Voivodeship, Poland
Burowiec (1960s–1970s). Since 1989, new construction has been relatively sparse. Post-1989 additions include three four-storey residential buildings on
Szopienice-Burowiec
SPARSE GRID
SPARSE GRID
Boy/Male
Afghan, Arabic, Iranian, Muslim, Parsi
Pious; Pure; Chaste; Holy
Surname or Lastname
English
English : variant of Speake.
Male
English
Short form of English unisex Paisley, PAISE means "church."Â
Surname or Lastname
English
English : metonymic occupational name for someone who made bags or purses or for an official in charge of expenditure, from Middle English purse (via Old English from Latin bursa).Scottish : variant of Purser.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Feel; Healthy; Touch
Surname or Lastname
English
English : from the Norman personal name Serlo, Germanic Sarilo, Serilo. This was probably originally a byname cognate with Old Norse Sorli, and akin to Old English searu ‘armor’, meaning perhaps ‘defender’, ‘protector’.
Surname or Lastname
English (Suffolk)
English (Suffolk) : unexplained.
Boy/Male
American, British, English
Gallant
Girl/Female
Hindu, Indian
Touch
Surname or Lastname
English
English : variant of Sparks.
Surname or Lastname
Irish (Kerry)
Irish (Kerry) : Anglicized form of Gaelic Mac Saoghair, which in turn may be a patronymic from a Gaelicized form of the Old English personal name Saeger (see 2 below).English : patronymic from a Middle English personal name Saher or Seir (see Sayer 1).Americanized form of French Cyr.Richard Sears came to Plymouth, MA, from England about 1630.
Surname or Lastname
English
English : patronymic from Spark 1.
Surname or Lastname
English
English : patronymic from Spear.
Surname or Lastname
English
English : patronymic from Spire 1.
Female
English
English variant form of French Cerise, SHARISE means "cherry."Â
Boy/Male
Anglo Saxon Welsh
Spares.
Surname or Lastname
English
English : variant of Spear.
Surname or Lastname
Portuguese
Portuguese : occupational name from soeiro ‘swineherd’, Latin suerius.English : patronymic from a nickname for someone with reddish hair, from Anglo-Norman French sor ‘chestnut (color)’.
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
SPARSE GRID
SPARSE GRID
Male
Czechoslovakian
, small.
Biblical
making speed to the spoil; he hastens to the prey
Boy/Male
Arabic, Muslim
Lion
Girl/Female
Hindu, Indian, Sanskrit
Pure; Purifying
Boy/Male
Hindu, Indian
Lord Subramanya
Girl/Female
Indian
The Moon
Boy/Male
Armenian, Australian, French, German, Hebrew
Armenian
Surname or Lastname
English
English : see Skeens.
Boy/Male
Indian, Malayalam, Tamil
God of Dev; Graceful
Girl/Female
Arabic, Muslim
Intelligence; Insight; Genius
SPARSE GRID
SPARSE GRID
SPARSE GRID
SPARSE GRID
SPARSE GRID
n.
A fine sieve; a searce.
adv.
Sparsely; scatteredly; here and there.
adv.
In a scattered or sparse manner.
v. t.
To emit in the form or likeness of sparks.
v. t.
To sift through a sarse.
v. t.
To sprinkle; to moisten by sprinkling; as, to sparge paper.
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
n.
One who spares.
v. t.
Being over and above what is necessary, or what must be used or reserved; not wanted, or not used; superfluous; as, I have no spare time.
superl.
Thinly scattered; set or planted here and there; not being dense or close together; as, a sparse population.
superl.
Large in bulk, or composed of large parts or particles; of inferior quality or appearance; not fine in material or close in texture; gross; thick; rough; -- opposed to fine; as, coarse sand; coarse thread; coarse cloth; coarse bread.
n.
Brilliancy; luster; as, the sparkle of a diamond.
superl.
Not refined; rough; rude; unpolished; gross; indelicate; as, coarse manners; coarse language.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
imp. & p. p.
of Parse
n.
One who parses.
n.
To emit sparks; to throw off ignited or incandescent particles; to shine as if throwing off sparks; to emit flashes of light; to scintillate; to twinkle; as, the blazing wood sparkles; the stars sparkle.
n.
The right of bowling again at a full set of pins, after having knocked all the pins down in less than three bowls. If all the pins are knocked down in one bowl it is a double spare; in two bowls, a single spare.
v. t.
To inclose in a hearse; to entomb.
imp. & p. p.
of Spare