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In parallel computing, the Geometric Arithmetic Parallel Processor (GAPP), invented by Polish mathematician Włodzimierz Holsztyński in 1981, was patented
Geometric Arithmetic Parallel Processor
Geometric_Arithmetic_Parallel_Processor
Central computer component that executes instructions
A central processing unit (CPU), also known as a central processor, main processor, or simply processor, is the primary processor in a given computer
Central_processing_unit
N-th root of the product of n numbers
the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of n {\displaystyle n} numbers is the nth
Geometric_mean
Topics referred to by the same term
manage privacy concerns German American Partnership Program Geometric-Arithmetic Parallel Processor GapP, A complexity class of counting in computer science
GAPP
Branch of mathematics
equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the 16th century later showed), arithmetic solutions
Geometry
Type of parallel processing
the use of SIMD-capable instructions. A later processor that used vector processing is the Cell processor used in the PlayStation 3, which was developed
Single instruction, multiple data
Single_instruction,_multiple_data
Inverse of the average of the inverses of a set of numbers
with the arithmetic mean, is the geometric mean to the power n. Thus the n-th harmonic mean is related to the n-th geometric and arithmetic means. The
Harmonic_mean
Use of a GPU for computations typically assigned to CPUs
Physics processing unit (PPU) Single instruction, multiple threads – Parallel computing execution model Vector processor – Computer processor which works
General-purpose computing on graphics processing units
General-purpose_computing_on_graphics_processing_units
Computer approximation for real numbers
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of
Floating-point_arithmetic
Analysis of variation in mechanical parts and assemblies
it fails to account for geometric misalignment allowed for by the tolerances; if a size dimension is placed between two parallel surfaces, it is assumed
Tolerance_analysis
between the arithmetic genus of a singular curve and the geometric genus of the desingularisation. The arithmetic genus is larger than the geometric genus,
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Natural number
1088/0026-1394/31/6/013. Peano, Giuseppe (1889). Arithmetices principia, nova methodo exposita [The principles of arithmetic, presented by a new method]. An excerpt
1
Number expressed in the base-2 numeral system
philosophical mathematics he admired. Of this parallel invention, Leibniz wrote in his "Explanation Of Binary Arithmetic" that "this restitution of their meaning
Binary_number
Device used for calculations
portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was
Calculator
Algorithm in numerical analysis
Kirchner, R.; Kulisch, U. (June 1988). "Accurate arithmetic for vector processors". Journal of Parallel and Distributed Computing. 5 (3): 250–270. doi:10
Kahan_summation_algorithm
A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures. Arithmetic geometry The use of algebraic geometry
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Spiral with constant distance from itself
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes
Archimedean_spiral
Sequence of operations for a task
only processor cycles on each processor but also the communication overhead between the processors. Some sorting algorithms can be parallelized efficiently
Algorithm
Number between two given numbers
Heronian mean of the numbers A and B is a weighted mean of their arithmetic and geometric means: H = 2 3 ⋅ A + B 2 + 1 3 ⋅ A B . {\displaystyle H={\frac
Heronian_mean
Branch of mathematics
restricted to regular arithmetic operations. For instance, the underlying set of the symmetry group of a geometric object is made up of geometric transformations
Algebra
Mathematical model of the physical space
one parallel line exists. Euclidean geometry is constructive. Postulates 1, 2, 3, and 5 assert the existence and uniqueness of certain geometric figures
Euclidean_geometry
Arithmetic operation
denoted with the plus sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division. The
Addition
Branch of computer science
stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered
Computational_geometry
Persian polymath and poet (1048–1131)
discovered which did not depend on geometric figures. This book was most likely titled the Difficulties of Arithmetic (Mushkilāt al-Ḥisāb), and is not extant
Omar_Khayyam
Probability distribution
referred to as the "geometric CV" (GCV), due to its use of the geometric variance. Contrary to the arithmetic standard deviation, the arithmetic coefficient of
Log-normal_distribution
than arithmetic. A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: There is one processor and
Communication-avoiding algorithm
Communication-avoiding_algorithm
Investment portfolio analysis technique
no. 4(July–August), pp. 39-44. Bacon, Carl, “Excess Returns – Arithmetic or Geometric?”, Journal of Performance Measurement, Spring 2002, pp. 23-31.
Performance_attribution
Ancient Chinese mathematics text
Japanese historian of mathematics Yoshio Mikami shortened the title to Arithmetic in Nine Sections. David Eugene Smith, in his History of Mathematics (Smith
The Nine Chapters on the Mathematical Art
The_Nine_Chapters_on_the_Mathematical_Art
Basic framework of mathematics
and theorems. Aristotle took a majority of his examples for this from arithmetic and from geometry, and his logic served as the foundation of mathematics
Foundations_of_mathematics
Basic concepts of algebra
arithmetic: arithmetic deals with specified numbers, whilst algebra introduces numerical variables (quantities without fixed values). In arithmetic,
Elementary_algebra
Australian and American mathematician (born 1975)
partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing, and
Terence_Tao
Number with a real and an imaginary part
complex plane. This allows a geometric interpretation of the complex numbers and their operations, and conversely some geometric objects and operations can
Complex_number
Algorithmic runtime requirements for common math procedures
Sarwate, D.V. (April 1978). "An improved parallel processor bound in fast matrix inversion". Information Processing Letters. 7 (3): 148–150. doi:10
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Theory of irregularities of distribution
on the following classic theorems: Geometric discrepancy theory The theorem of van Aardenne-Ehrenfest Arithmetic progressions (Roth, Sarkozy, Beck, Matousek
Discrepancy_theory
Algebraic structure with addition, multiplication, and division
order, are most directly accessible using modular arithmetic. For a fixed positive integer n, arithmetic "modulo n" means to work with the numbers Z/nZ =
Field_(mathematics)
Statistical method
various choices of statistics. Most bootstrap methods are embarrassingly parallel algorithms. That is, the statistic of interest for each bootstrap sample
Bootstrapping_(statistics)
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of
Ancient_Greek_mathematics
Probabilistic problem-solving algorithm
1016/j.jcp.2018.01.029. IEEE 754-2008 - IEEE Standard for Floating-Point Arithmetic. IEEE. 2008. pp. 1–70. doi:10.1109/IEEESTD.2008.4610935. ISBN 978-0-7381-5752-8
Monte_Carlo_method
List of notable software written in or for the C++ programming language
that uses Class Library for Numbers for implementing arbitrary-precision arithmetic GLFW — OpenGL and window management library HarfBuzz — text rendering
List of C++ software and tools
List_of_C++_software_and_tools
Ancient Greek mathematician (fl. 300 BC)
beginning with a set of 22 definitions for parity, prime numbers and other arithmetic-related concepts. Book 7 includes the Euclidean algorithm, a method for
Euclid
mathematical knowledge, including composite and prime numbers; arithmetic, geometric and harmonic means; and simplistic understandings of both the Sieve
History_of_mathematics
Measure of the joint variability
tend to show opposite behavior. The magnitude of the covariance is the geometric mean of the variances that are shared for the two random variables, where
Covariance
Wiener process Generative model Genetic epidemiology GenStat – software Geo-imputation Geodemographic segmentation Geometric Brownian motion Geometric data
List_of_statistics_articles
Setting of relativistic physics in geometric algebra
is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra provides a "unified, coordinate-free
Spacetime_algebra
Infinitely detailed mathematical structure
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly
Fractal
Generalization of the one-dimensional normal distribution to higher dimensions
and U is square, the resulting covariance matrix UΛUT is singular. Geometrically this means that every contour ellipsoid is infinitely thin and has zero
Multivariate normal distribution
Multivariate_normal_distribution
Data visualization
for comparing distributions between several groups or sets of data in parallel. Lastly, the overall structure of histograms and kernel density estimate
Box_plot
Branch of mathematics
better solution than the best one found so far by the algorithm. Interval arithmetic, interval mathematics, interval analysis, or interval computation, is
Global_optimization
Mathematical treatise by Euclid
the Elements is a collection in 13 books of definitions, postulates, geometric constructions, and theorems with their proofs that covers plane and solid
Euclid's_Elements
Methods used to find numerical solutions of ordinary differential equations
(2003). Geometric numerical integration illustrated by the Störmer–Verlet method. Acta Numerica, 12, 399-450. Nievergelt, Jürg (1964). "Parallel methods
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Computational physics simulation algorithm
simulates or imitates a physical process of compressing an assembly of hard particles. As the LSA may need thousands of arithmetic operations even for a few
Lubachevsky–Stillinger algorithm
Lubachevsky–Stillinger_algorithm
Branch of mathematics
into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of
Differential_geometry
Grouping a set of objects by similarity
the number of false negatives. The F M {\displaystyle FM} index is the geometric mean of the precision and recall P {\displaystyle P} and R {\displaystyle
Cluster_analysis
Statistical model for a binary dependent variable
X=x;\theta )}}+\log \Pr(Y=y\mid X=x)\right)\\[6pt]={}&-D_{\text{KL}}(Y\parallel Y_{\theta })-H(Y\mid X)\end{aligned}}} where H ( Y ∣ X ) {\displaystyle
Logistic_regression
compressed sensing, and image processing Izabella Łaba (born 1966), Polish-Canadian specialist in harmonic analysis, geometric measure theory, and additive
List_of_women_in_mathematics
Methodological basis for 3D CAD/CAM solid modeling and image rendering
basis for all geometric reasoning here. This figure shows a pinhole camera model for perspective effect in image processing and a parallel camera model
Ray_casting
Statistical method
coordinates. The parameters and variables of factor analysis can be given a geometrical interpretation. The data ( z a i {\displaystyle z_{ai}} ), the factors
Factor_analysis
Type of chart
irregular polygons, polar charts, and Kiviat diagrams. It is equivalent to a parallel coordinates plot, with the axes arranged radially. The radar chart is a
Radar_chart
Interference pattern
also serve; arithmetic averaging has the virtue of simplicity—with hopefully minimal damage to one's concepts of the printmaking process.) We now consider
Moiré_pattern
(combinatorics) Cameron–Erdős theorem (discrete mathematics) Corners theorem (arithmetic combinatorics) Courcelle's theorem (graph theory) De Bruijn–Erdős theorem
List_of_theorems
View of mathematicians to consolidate two or more theories into a more generalized one
by means of algorithms (or processes close to being algorithmic). Arithmetic is still taught that way. It was a parallel to the development of mathematical
Unifying theories in mathematics
Unifying_theories_in_mathematics
Algebra based on a vector space with a quadratic form
Clifford algebras. Clifford algebras are also sometimes referred to as geometric algebras, most often over the real numbers. Every nondegenerate quadratic
Clifford_algebra
Concept in linear algebra
\end{aligned}}} Since arithmetic and geometric means are equal if the variables are constant (see inequality of arithmetic and geometric means), we establish
Householder_transformation
Form of scientific experiment
healthcare literature, the major categories of RCT study designs are: Parallel-group – each participant is randomly assigned to a group, and all the participants
Randomized_controlled_trial
Historical development of geometry
fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions
History_of_geometry
Philosophical system based on the teachings of Pythagoras
linear geometrical figures replaced the dots, the combination of Babylonian algebra and Pythagorean arithmetic provided the basis for Greek geometric algebra
Pythagoreanism
Algorithms which recursively solve subproblems
for execution in multi-processor machines, especially shared-memory systems where the communication of data between processors does not need to be planned
Divide-and-conquer_algorithm
Sub-discipline of systems engineering that emphasizes dependability
for fatigue. The development of reliability engineering was here on a parallel path with quality. The modern use of the word reliability was defined by
Reliability_engineering
Field of knowledge
(such as matrices, modular integers, and geometric transformations), on which generalizations of arithmetic operations are often valid. The concept of
Mathematics
Probability distribution
inequality of arithmetic and geometric means that the geometric mean is lower than the mean. Similarly, the harmonic mean is lower than the geometric mean. The
Beta_distribution
Form of causal modeling that fit networks of constructs to data
several misspecifications. Direct-effect estimates are interpreted in parallel to the interpretation of coefficients in regression equations but with
Structural_equation_modeling
Type of Monte Carlo algorithms for signal processing and statistical inference
A. (2007). "Tracking deforming objects using particle filtering for geometric active contours". IEEE Transactions on Pattern Analysis and Machine Intelligence
Particle_filter
Number constructible via compass and straightedge
constructed using other processes. The set of constructible numbers forms a field: applying any of the four basic arithmetic operations to members of
Constructible_number
Nonparametric measure of rank correlation
they are treated in computing the rank correlation. Another approach parallels the use of the Fisher transformation in the case of the Pearson product-moment
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Geometric space with four dimensions
linked together into more complicated shapes that the full richness and geometric complexity of 4D spaces emerge. A hint of that complexity can be seen
Four-dimensional_space
Frequency with which an engineered system or component fails
(1988). "DFR Property of First-Passage Times and its Preservation Under Geometric Compounding". The Annals of Probability. 16 (1): 397–406. doi:10.1214/aop/1176991910
Failure_rate
Method of estimating the parameters of a statistical model, given observations
pp. 74–124. ISBN 0-19-850688-0. Kass, Robert E.; Vos, Paul W. (1997). Geometrical Foundations of Asymptotic Inference. New York, NY: John Wiley & Sons
Maximum_likelihood_estimation
Study of vector bundles, principal bundles, and fibre bundles
vector bundles, and so there are strong links between gauge theory and geometric analysis. These equations are often physically meaningful, corresponding
Gauge_theory_(mathematics)
Method of data analysis
concept by proposing Principal curves as the natural extension for the geometric interpretation of PCA, which explicitly constructs a manifold for data
Principal_component_analysis
Experiment in which information about the test is masked to reduce bias
"CONSORT 2010 explanation and elaboration: updated guidelines for reporting parallel group randomised trials". BMJ (Clinical Research Ed.). 340: c869. doi:10
Blinded_experiment
Branch of applied mathematics
space—hypothesized by Newton as a physically real entity of Euclidean geometric structure extending infinitely in all directions—while presuming absolute
Mathematical_physics
Bias in causal inference
participant pool to their groups (control, intervention, parallel), using a randomization process such as the use of a random number generator. For example
Confounding
Mathematical set with some added structure
always clear whether a given mathematical object should be considered as a geometric "space", or an algebraic "structure". A general definition of "structure"
Space_(mathematics)
Applying operations to whole sets of values simultaneously
CPUs sophisticated vector processors. Array processing is distinct from parallel processing in that one physical processor performs operations on a group
Array_programming
Pictorial representation of symmetry
groups', in Down under group theory, Proceedings of the Special Year on Geometric Group Theory, (Australian National University, Canberra, Australia, 1996)
Coxeter–Dynkin_diagram
Geometric mean and hyperbolic angle as coordinates in quadrant I
as the abscissas increased in a geometric series, the sum of the areas against the hyperbola increased in arithmetic series, and this property corresponded
Hyperbolic_coordinates
Theory of subatomic structure
with counting the numbers of solutions to geometric questions. Enumerative geometry studies a class of geometric objects called algebraic varieties which
String_theory
Concepts from linear algebra
λ {\displaystyle \lambda } (possibly a negative or complex number). Geometrically, vectors are multi-dimensional quantities with magnitude and direction
Eigenvalues_and_eigenvectors
Study of health and disease within a population
mass-action kinetics from chemistry to disease transmission in populations. In a parallel development during the 1920s, German-Swiss pathologist Max Askanazy and
Epidemiology
Function that measures dissimilarity between two probability distributions
q {\displaystyle p,q} or x , y {\displaystyle x,y} interprets them geometrically as points in a space, and μ 1 , μ 2 {\displaystyle \mu _{1},\mu _{2}}
Divergence_(statistics)
Determining where a point is in relation to a coplanar polygon
location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics, computer vision, geographic information
Point_in_polygon
Diagnostic plot of binary classifier ability
the dual (viz. predicting the prediction from the real class) and their geometric mean is the Matthews correlation coefficient.[citation needed] Whereas
Receiver operating characteristic
Receiver_operating_characteristic
(via Hypre and ML) and geometric multigrid Built-in preconditioners (ILU, diagonal, vanka, block) and LASPack serial, PETSc parallel, algebraic multigrid
List of finite element software packages
List_of_finite_element_software_packages
Study of the properties of codes and their fitness
networks" (PDF). In Eckmiller, R.; Hartmann, G.; Hauske, G. (eds.). Parallel processing in neural systems and computers (PDF). North-Holland. pp. 91–94.
Coding_theory
Geometry without using coordinates
two approaches are equivalent has been proved by Emil Artin in his book Geometric Algebra. Because of this equivalence, the distinction between synthetic
Synthetic_geometry
Sweep line algorithm
intersection points of two segments exactly, using arbitrary-precision arithmetic. However, it may be possible to speed up the calculations and comparisons
Bentley–Ottmann_algorithm
Statistical methods for comparing samples
inference context, proportions can be modeled using the Beta distribution. The parallel to two proportion z-test is performing similar inference using the difference
Two-proportion_Z-test
Array of logic gates that are reprogrammable
processor in combination with Atmel's programmable logic architecture. The Microsemi SmartFusion devices incorporate an ARM Cortex-M3 hard processor core
Field-programmable_gate_array
design and analysis of parallel algorithms and scheduling techniques. 2006 Thomas Robertazzi For contributions to parallel processor scheduling. 2023 Miguel
List of fellows of IEEE Computer Society
List_of_fellows_of_IEEE_Computer_Society
Method of curve fitting
{y-y_{0}}{x-x_{0}}}={\frac {y_{1}-y_{0}}{x_{1}-x_{0}}},} which can be derived geometrically from the figure on the right. It is a special case of polynomial interpolation
Linear_interpolation
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
Biblical
parables; governing
Girl/Female
Biblical
A parable, governing.
Biblical
a parable; governing
Girl/Female
Arabic, Muslim
Example; Allegory; Parable
Boy/Male
Shakespearean
All's Well That Ends Well.' A follower of Bertram, Count of Rousillon.
Boy/Male
Greek
Greek surname. Euclid was an early developer of geometry theories.
Surname or Lastname
English
English : occupational name from Middle English combere, an agent derivative of Old English camb ‘comb’, referring perhaps to a maker or seller of combs, or to someone who used them to prepare wool or flax for spinning. This was an alternative process to carding, and caused the wool fibers to lie more or less parallel to one another, so that the cloth produced had a hard, smooth finish without a nap.English : variant of Coomber.Probably an Americanized spelling of German Kommer or Kammer.
Girl/Female
Muslim
Example, Allegory, Parable
Girl/Female
Biblical
Parables, governing.
Male
German
Old German name, GOMERIC means "man-power."
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
Boy/Male
Muslim
Vision, Propitious, Auspicious, Prudent, Bringer of glad tidings
Boy/Male
Hindu
Guide
Girl/Female
Australian, Jamaican
Aunt; Princess
Boy/Male
Muslim
Trustworthy
Boy/Male
Tamil
Victorious
Girl/Female
Hindu
Madhur
Girl/Female
Tamil
Tanwesha | தாநà¯à®µà¯‡à®·à®¾Â
Boy/Male
Biblical
Nuptial; the god of marriage.
Girl/Female
Muslim
Bitter
Female
Welsh
Variant spelling of Welsh Enid, ENIT means "soul."
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
GEOMETRIC ARITHMETIC-PARALLEL-PROCESSOR
a.
Of or pertaining to arithmetic; according to the rules or method of arithmetic.
imp. & p. p.
of Parallel
n.
Arithmetic.
pl.
of Geometry
v. i.
To be parallel; to correspond; to be like.
a.
Alt. of Geometrical
v. t.
To place or set so as to be parallel; to place so as to be parallel to, or to conform in direction with, something else.
n.
One of the imaginary circles on the surface of the earth, parallel to the equator, marking the latitude; also, the corresponding line on a globe or map.
a.
Extended in the same direction, and in all parts equally distant; as, parallel lines; parallel planes.
a.
Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.
a.
Having opposite surfaces exactly plane and parallel, as a piece of glass.
v. t.
To produce or adduce as a parallel.
n.
A line which, throughout its whole extent, is equidistant from another line; a parallel line, a parallel plane, etc.
v. i.
To investigate or apprehend geometrical quantities or laws; to make geometrical constructions; to proceed in accordance with the principles of geometry.
v. t.
To represent by parable.
a.
Pertaining to geometry.
a.
Continuing a resemblance through many particulars; applicable in all essential parts; like; similar; as, a parallel case; a parallel passage.
n.
A comparison made; elaborate tracing of similarity; as, Johnson's parallel between Dryden and Pope.
adv.
In a parallel manner; with parallelism.
a.
Of or pertaining to aerometry; as, aerometric investigations.