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Computational error due to rounding numbers
In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and
Round-off_error
Move in gymnastics
A roundoff is a move in gymnastics similar to a cartwheel, except the gymnast lands with two feet placed together on the ground instead of one foot at
Roundoff
Type of vault in artistic gymnastics
gymnast performs a low skipping motion called the hurdle to begin the roundoff. The roundoff, a quick cartwheel, is then performed onto the springboard with
Yurchenko_vault_family
Algorithms which recursively solve subproblems
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more
Divide-and-conquer_algorithm
Upper bound on rounding error in floating-point arithmetic
epsilon is dependent on the type of rounding used and is also called unit roundoff, which has the symbol bold Roman u {\displaystyle \mathbf {u} } . The two
Machine_epsilon
analysis, one or more guard digits can be used to reduce the amount of roundoff error. Suppose that the final result of a long, multi-step calculation
Guard_digit
Use of numerical analysis to estimate derivatives of functions
{e(x+h)-e(x-h)}{2h}} _{\text{Roundoff error}}-\underbrace {{\frac {f^{(3)}(c)}{6}}h^{2}} _{\text{Truncation error}}.} Assuming that the roundoff errors are bounded
Numerical_differentiation
Computer approximation for real numbers
error analysis of floating-point algorithms. It is also known as unit roundoff or machine epsilon. Usually denoted Εmach, its value depends on the particular
Floating-point_arithmetic
Algorithmic technique
and adding the two sums: a divide and conquer algorithm. Its worst-case roundoff errors grow asymptotically as at most O(ε log n), where ε is the machine
Pairwise_summation
Floating-point number formats
formats. Extended-precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format
Extended_precision
Algorithm in numerical analysis
error that grows as n {\displaystyle {\sqrt {n}}} for random inputs (the roundoff errors form a random walk). With compensated summation, using a compensation
Kahan_summation_algorithm
Aerial maneuver in various sports
control of the landing. In gymnastics, some coaches describe a Barani as a roundoff without hands or, mostly on beam, a front somersault with a half twist
Barani_flip
guaranteed enclosure, affine arithmetic operations must account for the roundoff errors in the computation of the resulting coefficients z j {\displaystyle
Affine_arithmetic
Acrobatic move
such as a tuck or layout. Similarly, another rotational move (e.g., a roundoff) may precede a handspring in order to develop sufficient momentum for the
Handspring_(gymnastics)
Acrobatic jump
often executed immediately following another rotational move, such as a roundoff or handspring, to take advantage of the angular momentum generated by the
Flip_(acrobatic)
standing position or immediately following another similar move, such as a roundoff. Flash switch: In this variation, also known as double flash or scissor
Flashkick
Sport requiring strength and flexibility
25 metres (82 ft) runway, to take off onto a spring board performing a roundoff handspring or front handspring entry onto a vault board). They then land
Gymnastics
American gymnast (born 1992)
leap (C) to back tuck or pike (C), roundoff to double pike dismount (E) 5.7 (5.8*) 14.266 Floor Exercise Roundoff back handspring to full-in double pike
Mackenzie_Caquatto
Compressed image file format
transformation from RGB to YCbCr, which is slightly lossy in practice because of roundoff error. JPEG XR specifies a lossless colorspace transformation, namely YCoCg-R
JPEG_XR
Soviet artistic gymnast
pass on floor at the 1980 Olympic Games was a roundoff 1.5-twisting layout immediately into a roundoff back handspring double pike. At the 1980 Olympics
Natalia_Shaposhnikova
American artistic gymnast
sheep jump (D); switch split ring leap (E); side somi (D); front tuck (D); roundoff + Arabian double front dismount (G) 6.5 15.300 Floor Exercise Front handspring
Rebecca_Bross
is a long piece of material attached to a stick. Rings See still rings. Roundoff A move similar to a cartwheel where the gymnast pushes off the ground and
Glossary_of_gymnastics_terms
Intel SIMD processor supplementary instruction sets introduced by Intel
intermediate results with 80 bits of precision, by default, to minimise roundoff error in numerically unstable algorithms (see IEEE 754 design rationale
SSE2
American surface-to-air missile system since 1981
January 6, 2018. Retrieved January 5, 2018. Skeel, Robert (July 1992). "Roundoff Error and the Patriot Missile". SIAM News. 25 (4). Society for Industrial
MIM-104_Patriot
Mathematical optimization algorithm
be slow and the quality of the approximate solution may be sensitive to roundoff errors. Finding a good preconditioner is often an important part of using
Conjugate_gradient_method
Mass per unit volume of the Earth's atmosphere
to the troposphere Total values may not add up to exactly 100% due to roundoff and uncertainty. ppmv: parts per million by volume. Volume fraction is
Density_of_air
Style of dance with acrobatics
Individual Acro Dance Tricks : Bridge / Backbend Cartwheel Roundoff Front walkover Back walkover Valdez Leg Extensions Handstand Bow and Arrow Handstand
Acro_dance
Ratio of the desired signal to the background noise
Stuttgart Bernard Widrow, István Kollár (2008-07-03), Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications
Signal-to-noise_ratio
Shell command for comparing file content
variant of diff that ignores differences in floating point calculations with roundoff errors and whitespace, both of which are generally irrelevant to source
Diff
Device for suppressing part of a discretely-sampled signal
J. O. Smith III, Direct Form II L. B. Jackson, "On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters," Bell Sys. Tech. J., vol. 49
Digital_filter
Ability of numerical algorithms to remain accurate under small changes of inputs
diffusion. Numerical diffusion is a mathematical term which ensures that roundoff and other errors in the calculation get spread out and do not add up to
Numerical_stability
Important algorithms in numerical statistics
summation scheme for the sum() function, making it resistant to repeated roundoff error. Many numerically oriented languages provide similar constructs.
Algorithms for calculating variance
Algorithms_for_calculating_variance
American computer and word processing company (1951–1999)
discrete transistors. It performed multiplication by adding logarithms, and roundoff in the display conversion was noticeable: 2 × 2 yielded 3.999999999. From
Wang_Laboratories
American artistic gymnast (born 1995)
kept the Amanar as her first vault and upgraded her second vault to the roundoff half-on layout full. She also increased her difficulty scores on the uneven
McKayla_Maroney
Second order recursive digital linear filter
J. O. Smith III, Direct Form II L. B. Jackson, "On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters," Bell Sys. Tech. J., vol. 49
Digital_biquad_filter
errors, also called numerical errors, include both truncation errors and roundoff errors. router A networking device that forwards data packets between computer
Glossary_of_computer_science
Canadian computer scientist (born 1947)
representation of the rational numbers that allows easier arithmetic and precludes roundoff error.[citation needed] He was involved with developing international standards
Eric_Hehner
List of x86 microprocessor instructions
remainder computation done by the FPREM instruction is always exact with no roundoff errors. For the FSCALE instruction on 8087 and 80287, st(1) is required
List_of_x86_instructions
Acrobatic discipline
Handstand Cartwheel Sideways Rolls using hands and Feet In Handstand Position Roundoff, Single handed Cartwheel, Helicopter Flips Forward Rolls Front Flips Forward
Tricking_(martial_arts)
American artistic gymnast
leg above horizontal + Popa; roundoff + triple twist dismount. Floor exercise (SV: 10.0): Popa + tuck jump 2/1; roundoff + back handspring + 2½ twist
Courtney_McCool
Algorithms for zeros of functions
However, it may fail to converge in some naive implementations due to roundoff errors that may lead to a wrong sign for f(c). Typically, this may occur
Root-finding_algorithm
C programming language standard, 1999 revision
William Kahan (11 January 2006). "How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?" (PDF). Peter Bright (29 June 2013). "C99
C99
report IMTEC 92-26". US Government Accounting Office. Skeel, Robert. "Roundoff Error and the Patriot Missile". SIAM News, volume 25, nr 4. Archived from
List_of_software_bugs
Soviet and Russian gymnast
Omelianchik debuted her new vault which introduced the half-on technique in the roundoff family of vaults. She also showcased a new floor routine to Ballet Russe
Oksana_Omelianchik
Professional wrestling move
mat landing on the opponent. This move can be set up by preceding with a roundoff. WWE wrestler Apollo Crews uses this as his finishing maneuver. Jeff Cobb
Moonsault
Device that measures magnetism
resolve. This includes quantization error which is caused by recording roundoff and truncation of digital expressions of the data. Absolute error is the
Magnetometer
defect, which is most likely due to both the use of integer coordinates and roundoff errors. Because Tgif uses Xlib (which predated modern Unicode support)
Tgif_(program)
Second edition of the IEEE 754 floating-point standard
Decimal William Kahan's paper on How Futile are Mindless Assessments of Roundoff in Floating-Point Computation ISO Language Independent Arithmetic Standard
IEEE_754-2008_revision
American baseball player (born 1957)
reaction that "I wanted to do a couple of cartwheels, a backflip and a roundoff." Castillo was also on base in Game 5 (the final game) when Kirk Gibson
Marty_Castillo
Lists of values of mathematical functions
John Wiley & Sons. Manfred Tasche and Hansmartin Zeuner (2002) "Improved roundoff error analysis for precomputed twiddle factors", Journal for Computational
Trigonometric_table
Replacing a number with a simpler value
"Monte Carlo Arithmetic: a framework for the statistical analysis of roundoff errors". IEEE Computation in Science and Engineering. Borman, Phil; Chatfield
Rounding
American mathematician and information theorist (1915–1998)
unstable, so that under certain conditions the result could be swamped by roundoff noise. Hamming developed an improved version, the Hamming predictor-corrector
Richard_Hamming
with real arguments. The map depends on only the one constant α. Due to roundoff error, successive applications of the modulo operator will yield zero after
Kaplan–Yorke_map
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
difficult to compute because most trajectories are unstable and sensitive to roundoff errors and details of the numerical integration. Gutzwiller applied the
Quantum_chaos
Concept in linear algebra
{\gamma _{n}}}:={\frac {cnu}{1-cnu}}} (where u {\displaystyle u} is unit roundoff, n {\displaystyle n} the size of the matrix P {\displaystyle P} , and c
Householder_transformation
condition to execute this skill, some skills are recommended; these include: roundoff, back handspring, back tuck, layout, and a half twisting layout. The skill
Full_twisting_layout
Concept in mathematics
quadratic function the minimum is reached within N iterations (excepting roundoff error), but a non-quadratic function will make slower progress. Subsequent
Nonlinear conjugate gradient method
Nonlinear_conjugate_gradient_method
Chinese gymnast (born 2000)
handspring layout full, the handspring layout 1.5 (Chusovitina) and the roundoff half-turn layout double full (Biles). Luo also placed the lowest in floor
Luo_Huan
Japanese artistic gymnast
technique called the "Tsukahara vault". This vault is generally described as a roundoff over the horse/table into a backward salto, with or without twist. However
Mitsuo_Tsukahara
Numerical eigenvalue calculation
judging the usefulness of implementing an algorithm on a computer with roundoff. For the Lanczos algorithm, it can be proved that with exact arithmetic
Lanczos_algorithm
Variant of fast Fourier transform
{\displaystyle z\leftarrow {\text{round}}(z)} , optionally checking the roundoff error is no greater than 0.4 (greater indicates too many integer bits stuffed
Irrational base discrete weighted transform
Irrational_base_discrete_weighted_transform
Computational physics simulation algorithm
continue the calculations when inter-collision runs are smaller than the roundoff error. The LSA is efficient in the sense that the events are processed
Lubachevsky–Stillinger algorithm
Lubachevsky–Stillinger_algorithm
American electrical engineer (1929–2025)
Prentice-Hall, Inc., 1994. 2008 B. Widrow and I. Kollar. Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications
Bernard_Widrow
Chinese gymnast (born 1979)
giants, Tkatchev, double layout Balance beam: one-arm handstand mount, roundoff—layout to two feet, switch leap—double stag ring leap—back dive ¼ turn
Mo_Huilan
American artistic gymnast
punch front, beat jump - switch leap, back dive 1/4, back hip circle - roundoff, flip flop, double tuck (9.9 SV) Floor exercise: Round-off + back handspring
Terin_Humphrey
Study of kind and quantity of error
basic approach is to show that although the calculated result, due to roundoff errors, will not be exactly correct, it is the exact solution to a nearby
Error_analysis_(mathematics)
Estimation method that minimizes the mean square error
covariance update equations, thus improving the numerical robustness against roundoff errors. The update can be implemented iteratively as: w k + 1 ( ℓ ) = C
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Moves in gymnastics
on balance beam, and two on floor exercise. Biles debuted her vault, a roundoff, back handspring with half turn entry; front stretched somersault with
Gymnastics elements named after Simone Biles
Gymnastics_elements_named_after_Simone_Biles
Programming language
check that it was numerically equivalent (or within the floating point roundoff error) to the correct answer. The language included a pre-defined constant
TUTOR
<0\end{cases}}} where ε is a positive parameter depending on the machine's unit roundoff, and the factorization continues with the boosted pivot. This can be achieved
SPIKE_algorithm
Russian artistic gymnast
Horizontal; sheep jump; onodi, flip-flop, layout stepout; sissone, split jump; roundoff (RO) double pike dismount 6.0 Floor Exercise Double Layout; 2½ twist punch
Ksenia_Semyonova
Method of numerical integration
method. Modification 4, not implemented here, contains provisions for roundoff error that allows for raising the ε to the minimum allowed by current precision
Adaptive_Simpson's_method
American artistic gymnast
Layout in combination; Piked Front + Jump in combination; Tucked Barani; Roundoff + Back Handspring + Double Tuck Dismount. Uneven Bars: Giant One and a
Vanessa_Atler
Ukrainian artistic gymnast
balance beam, her skills included a front tuck, back tuck, standing Arabian, roundoff–back layout, and double tuck dismount. In 2008, she competed at the Voronin
Yana_Demyanchuk
after Guillermo Alvarez (US) Amanar (vault) – Yurchenko family vault, roundoff on and 21⁄2 twists off, after Simona Amânar (Romania) Araújo (balance beam
List of sports terms named after people
List_of_sports_terms_named_after_people
Indian engineer
Roy (December 1982). "FIR Filter Structures Having Low Sensitivity and Roundoff Noise". IEEE Transactions on Acoustics, Speech, and Signal Processing.
S._C._Dutta_Roy
Canadian artistic gymnast
Layout to Back Layout; Illusion; Double Turn; Front Tuck; Switch Leap to Roundoff Aerial; Double Back Somersault Dismount Floor Exercise - Triple Turn; Full
Elyse_Hopfner-Hibbs
Mexican artistic gymnast
compete on two events. She scored 12.400 on balance beam, competing a roundoff Patterson dismount and 13.733 on floor. The music she used on her floor
Elsa_García_(gymnast)
ROUNDOFF
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Girl/Female
Indian, Telugu
Boundary
Boy/Male
Tamil
Sreeyan | à®·à¯à®°à¯€à®¯à®¾à®¨
Lord Vishnu
Girl/Female
English American Scottish
From the linden tree island.
Boy/Male
Indian, Sanskrit
Lord of the Gods
Boy/Male
Tamil
Runithya | à®°à¯à®¨à¯€à®¤à¯à®¯
Boy/Male
English
Noble or famous.
Girl/Female
Celebrity, Indian
Shinning Light
Girl/Female
British, English
Warrior Maid
Girl/Female
Hebrew Russian
God shall redeem.
Girl/Female
Hindu, Indian
Mother with Love
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