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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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
Species of flowering plant
combination of sparse long eglandular hairs (which are black at the base and white at the tip), numerous short glandular hairs, and sparse white stellate
Hieracium_attenboroughianum
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
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
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
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
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
Disambiguation article
with each field stored as a separate array Sparse array, with most elements omitted, to store a sparse matrix Variable-length array or various related
Array
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
Multifaceted crossword puzzle
crosswords, and sometimes two sets of clues are given for a single puzzle grid.[citation needed] Cryptic crossword puzzles come in two main types: the basic
Cryptic_crossword
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
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
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
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
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
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
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
Remote procedure call for grid computing
libraries or studies on heuristics and resolution methods for sparse linear algebra like GridTLSE. This approach of providing computation services through
GridRPC
2011 nuclear accident in Japan
cause was the Tōhoku earthquake and tsunami, which resulted in electrical grid failure and damaged nearly all of the power plant's backup energy sources
Fukushima_nuclear_accident
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
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
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
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
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
Commemorative coins of the Eurozone
Description: The inner part of the coin has a mosaic design, with the more sparsely set pieces on the right forming a cartographic likeness of Finland. The
2_euro_commemorative_coins
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
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
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
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
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
Capital and largest city of Kyrgyzstan
mountain chain that runs north-west to south-east. In the winter months, sparse snow storms and frequent heavy fog are the dominating features. There are
Bishkek
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
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
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
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
downtown area, which began developing in the 1840s with a planned street grid and squares, features a variety of buildings, including late-19th- and early-20th-century
Architecture_of_Katowice
Large permanent human settlement
potential to have a smaller ecological footprint per inhabitant than more sparsely populated areas. Therefore, compact cities are often referred to as a crucial
City
Method in computer graphics
the idea was adapted into geometry clipmaps, which use nested regular grids centered on the viewer and update them incrementally as the viewpoint moves
Clipmap
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
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
Bringing electrical power to rural areas
communities are suffering from colossal market failures as the national grids fall short of their demand for electricity. As of 2019, 770 million people
Rural_electrification
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
Ancient Greek city in Asia-Minor
including the sanctuary of Apollo at Didyma, remnants of the city's distinctive grid plan, and evidence of long-term agricultural and rural management. Throughout
Miletus
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
Database management system
briefly, Essbase requires the developer to tag dimensions as "dense" or "sparse". The system then arranges data to represent the hypercube into "blocks"
Essbase
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)
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
Country in Southern Africa
shrubs, and acacia, mainly camel-thorn (Vachellia erioloba). Vegetation is sparse towards the north-west because of low rainfall. There are numerous species
South_Africa
Supply energy using single wire with earth as return
transmission line which supplies single-phase electric power from an electrical grid to remote areas at lowest cost. The earth (or sometimes a body of water)
Single-wire_earth_return
Process of achieving a goal by overcoming obstacles
; Barrett, H. Clark (2005). "Functional Fixedness in a Technologically Sparse Culture". Psychological Science. 16 (1). SAGE Publications: 1–5. doi:10
Problem_solving
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
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
Concepts from linear algebra
convergence than the QR algorithm.[citation needed] For large Hermitian sparse matrices, the Lanczos algorithm is one example of an efficient iterative
Eigenvalues_and_eigenvectors
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
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
Most populous city in Canada
extensive bus network that serves parts of the city many not served by the sparse subway network. The TTC bus system had an annual ridership of over 389 million
Toronto
geographic area and administered by the neighboring nations. Most islands are sparsely populated, with some being barren, and some utilized for communication
List of islands in the Persian Gulf
List_of_islands_in_the_Persian_Gulf
Measurement of graph sparsity
degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph
Degeneracy_(graph_theory)
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
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
Array of numbers
ISBN 978-0-486-13930-2 Scott, J.; Tůma, M. (2023), "Sparse Matrices and Their Graphs", Algorithms for Sparse Linear Systems, Nečas Center Series, Cham: Birkhäuser
Matrix_(mathematics)
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
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
Technique to solve partial differential equations
physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with
Physics-informed neural networks
Physics-informed_neural_networks
Puzzle video game
player progresses by solving puzzles, which are based on interactions with grids presented on panels around the island or paths hidden within the environment
The_Witness_(2016_video_game)
SPARSE GRID
SPARSE GRID
Boy/Male
American, British, English
Gallant
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.
Surname or Lastname
English
English : variant of Spear.
Female
English
English variant form of French Cerise, SHARISE means "cherry."Â
Girl/Female
Hindu, Indian
Touch
Surname or Lastname
English
English : variant of Sparks.
Boy/Male
Anglo Saxon Welsh
Spares.
Boy/Male
Afghan, Arabic, Iranian, Muslim, Parsi
Pious; Pure; Chaste; Holy
Surname or Lastname
English
English : variant spelling of Pass.French : possibly a nickname from passe ‘sparrow’.
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 : patronymic from Spear.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Feel; Healthy; Touch
Surname or Lastname
English
English : variant of Speake.
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
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
Surname or Lastname
English
English : patronymic from Spire 1.
Surname or Lastname
English (Suffolk)
English (Suffolk) : unexplained.
Male
English
Short form of English unisex Paisley, PAISE means "church."Â
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.
SPARSE GRID
SPARSE GRID
Boy/Male
Arthurian Legend
Killed by Percival.
Girl/Female
Tamil
Arnika | à®…à®°à¯à®¨à®¿à®•à®¾
Goddess Durga
Boy/Male
Hebrew, Hindu, Indian
Water
Boy/Male
Muslim
Helper in the religion
Girl/Female
Indian, Parsi
Full Moon
Boy/Male
African, American, Australian, Biblical, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hebrew, Jamaican, Latin, Polish, Portuguese, Swedish
Obeys; God has Listen; Listening Intently; To be Heard; He who has Heard
Boy/Male
Hindu, Indian
Rising Upward; Progressing
Boy/Male
English
Son of Dick.
Boy/Male
Muslim
Liberal, Eternal
Boy/Male
Hindu
One who takes care the universe, Caretaker of the world God
SPARSE GRID
SPARSE GRID
SPARSE GRID
SPARSE GRID
SPARSE GRID
v. t.
Scanty; not abundant or plentiful; as, a spare diet.
n.
One who parses.
v. t.
To inclose in a hearse; to entomb.
n.
A fine sieve; a searce.
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.
imp. & p. p.
of Spare
n.
One who spares.
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.
imp. & p. p.
of Parse
v. t.
To sift through a sarse.
n.
Brilliancy; luster; as, the sparkle of a diamond.
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.
adv.
In a scattered or sparse manner.
superl.
Not refined; rough; rude; unpolished; gross; indelicate; as, coarse manners; coarse language.
adv.
Sparsely; scatteredly; here and there.
superl.
Thinly scattered; set or planted here and there; not being dense or close together; as, a sparse population.
v. t.
Held in reserve, to be used in an emergency; as, a spare anchor; a spare bed or room.
v. t.
To sprinkle; to moisten by sprinkling; as, to sparge paper.
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.
v. t.
To emit in the form or likeness of sparks.