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The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations. In the case of matrix algorithms, a pivot entry is usually required to be at least distinct from zero, and often distant from it; in this case finding this element is called pivoting. Pivoting may be followed by an interchange of rows or columns to bring the pivot to a fixed position and allow the algorithm to proceed successfully, and possibly to reduce round-off error. It is often used for verifying row echelon form.

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The Pivot 14 bindings that you are looking at have a.5 degree ramp. The lowest binding ramp that we offer is.2 degrees on our Pivot 18 bindings. If you have any further questions, please feel free to send us an email directly at inforossiusa@rossignol.com Thank You! The pivot point defines the position around which objects or components are rotated and scaled. By default, the pivot point of an object or group of objects/components is located at its center. If you want to rotate an around a specific point, like a forearm rotates from an elbow, you need to adjust the pivot's position. Custom Pivot mode is the default method for setting object and component.

Pivoting might be thought of as swapping or sorting rows or columns in a matrix, and thus it can be represented as multiplication by permutation matrices. However, algorithms rarely move the matrix elements because this would cost too much time; instead, they just keep track of the permutations.

Overall, pivoting adds more operations to the computational cost of an algorithm. These additional operations are sometimes necessary for the algorithm to work at all. Other times these additional operations are worthwhile because they add numerical stability to the final result.

Examples of systems that require pivoting[edit]

In the case of Gaussian elimination, the algorithm requires that pivot elements not be zero.Interchanging rows or columns in the case of a zero pivot element is necessary. The system below requires the interchange of rows 2 and 3 to perform elimination.

{displaystyle left[{begin{array}{ccc|c}1&-1&2&80&0&-1&-110&2&-1&-3end{array}}right]}

The system that results from pivoting is as follows and will allow the elimination algorithm and backwards substitution to output the solution to the system.

{displaystyle left[{begin{array}{ccc|c}1&-1&2&80&2&-1&-30&0&-1&-11end{array}}right]}

Furthermore, in Gaussian elimination it is generally desirable to choose a pivot element with large absolute value. This improves the numerical stability. The following system is dramatically affected by round-off error when Gaussian elimination and backwards substitution are performed.

{displaystyle left[{begin{array}{cc|c}0.00300&59.14&59.175.291&-6.130&46.78end{array}}right]}

This system has the exact solution of x₁ = 10.00 and x₂ = 1.000, but when the elimination algorithm and backwards substitution are performed using four-digit arithmetic, the small value of a₁₁ causes small round-off errors to be propagated. The algorithm without pivoting yields the approximation of x₁ ≈ 9873.3 and x₂ ≈ 4. In this case it is desirable that we interchange the two rows so that a₂₁ is in the pivot position

{displaystyle left[{begin{array}{cc|c}5.291&-6.130&46.780.00300&59.14&59.17end{array}}right].}

Considering this system, the elimination algorithm and backwards substitution using four-digit arithmetic yield the correct values x₁ = 10.00 and x₂ Torrent movie download. = 1.000.

Partial and complete pivoting[edit]

In partial pivoting, the algorithm selects the entry with largest absolute value from the column of the matrix that is currently being considered as the pivot element. Partial pivoting is generally sufficient to adequately reduce round-off error. However, for certain systems and algorithms, complete pivoting (or maximal pivoting) may be required for acceptable accuracy. Complete pivoting interchanges both rows and columns in order to use the largest (by absolute value) element in the matrix as the pivot. Complete pivoting is usually not necessary to ensure numerical stability and, due to the additional cost of searching for the maximal element, the improvement in numerical stability that it provides is typically outweighed by its reduced efficiency for all but the smallest matrices. Hence, it is rarely used.^[1]

Scaled pivoting[edit]

A variation of the partial pivoting strategy is scaled pivoting. In this approach, the algorithm selects as the pivot element the entry that is largest relative to the entries in its row. This strategy is desirable when entries' large differences in magnitude lead to the propagation of round-off error. Scaled pivoting should be used in a system like the one below where a row's entries vary greatly in magnitude. In the example below, it would be desirable to interchange the two rows because the current pivot element 30 is larger than 5.291 but it is relatively small compared with the other entries in its row. Without row interchange in this case, rounding errors will be propagated as in the previous example.

{displaystyle left[{begin{array}{cc|c}30&591400&5917005.291&-6.130&46.78end{array}}right]}

Pivot position[edit]

A pivot position in a matrix, A, is a position in the matrix that corresponds to a row–leading 1 in the reduced row echelon form of A. Since the reduced row echelon form of A is unique, the pivot positions are uniquely determined and do not depend on whether or not row interchanges are performed in the reduction process. Also, the pivot of a row must appear to the right of the pivot in the above row in row echelon form.

References[edit]

This article incorporates material from Pivoting on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

^Edelman, Alan, 1992. The Complete Pivoting Conjecture for Gaussian Elimination is False. Mathematica Journal 2, no. 2: 58-61.

R. L. Burden, J. D. Faires, Numerical Analysis, 8th edition, Thomson Brooks/Cole, 2005. ISBN0-534-39200-8
G. H. Golub, C. F. Loan, Matrix Computations, 3rd edition, Johns Hopkins, 1996. ISBN0-8018-5414-8.
Fukuda, Komei; Terlaky, Tamás (1997). Thomas M. Liebling; Dominique de Werra (eds.). 'Criss-cross methods: A fresh view on pivot algorithms'. Mathematical Programming, Series B. Papers from the 16th International Symposium on Mathematical Programming held in Lausanne, 1997. 79 (1–3): 369–395. CiteSeerX10.1.1.36.9373. doi:10.1007/BF02614325. MR1464775. Postscript preprint.
Terlaky, Tamás; Zhang, Shu Zhong (1993). 'Pivot rules for linear programming: A Survey on recent theoretical developments'. Annals of Operations Research. Degeneracy in optimization problems. 46–47 (1): 203–233. CiteSeerX10.1.1.36.7658. doi:10.1007/BF02096264. ISSN0254-5330. MR1260019.

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Related to pivot: Pivot table

piv·ot

(pĭv′ət) n.

1. A short rod or shaft on which a related part rotates or swings.

2. A person or thing on which something depends; the central or crucial factor: 'The pivot of the whole affair was the stupidity of some admiral' (Joseph Conrad).

4. A dramatic change in policy, position, or strategy: 'President Obama's decision to cancel a planned week-long trip to Asia .. is raising questions across Washington about the administration's vaunted pivot to Asia' (Howard LaFranchi).

a. A person around which a formation of marching people turns.

b. Sports A player who plays at the center of the offense.

6. Basketball

a. A position taken by an offensive player usually facing away from the basket near the foul line to relay passes, attempt a shot, or set screens.

b. The stationary foot around which the ball handler is allowed to pivot without dribbling.

v.tr.

1. To mount on, attach by, or provide with a pivot or pivots.

2. To cause to rotate, revolve, or turn: pivoted the telescope toward the island.

intr.

2. To depend or be centered: 'The plot .. lacks direction, pivoting on Hamlet's incertitude' (G. Wilson Knight).

3. To make a dramatic change in policy, position, or strategy: 'If you start pivoting, you're not being honest with people' (Donald Trump).

[French, from Old French ; akin to perhaps akin to Catalan piu, pivot, perhaps from piu, chirp (from the creaking sounds made by something turning on a pivot ).]

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

pivot

(ˈpɪvət) n

1. (Mechanical Engineering) a short shaft or pin supporting something that turns; fulcrum

2. (Mechanical Engineering) the end of a shaft or arbor that terminates in a bearing

3. a person or thing upon which progress, success, etc, depends

4. (Military) the person or position from which a military formation takes its reference, as when altering position

5. (tr) to mount on or provide with a pivot or pivots

[C17: from Old French; perhaps related to Old Provençal pua tooth of a comb]

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

piv•ot

(ˈpɪv ət)
n.

1. a pin, point, or short shaft on the end of which something rests and turns, or upon and around which something rotates or oscillates.

2. the end of a shaft or arbor, resting and turning in a bearing.

3. a person or thing on which something turns, hinges, or depends: She was the pivot of the campaign's success.

4. the person in a line, as of troops on parade, whom the others use as a point around which to wheel or maneuver.

6. Basketball.

a. an offensive position in the front court, usu. played by the center, in which the player stands facing away from the offensive basket.

v.i.

7. to turn on or as if on a pivot.

v.t.

8. to mount on, attach by, or provide with a pivot or pivots.

[1605–15; < French pivot (n.), pivoter (v.), Old French]

pivot

Past participle: pivoted
Gerund: pivoting

Imperative
pivot
pivot

Present
I pivot
you pivot
he/she/it pivots
we pivot
you pivot
they pivot

Preterite
I pivoted
you pivoted
he/she/it pivoted
we pivoted
you pivoted
they pivoted

Present Continuous
I am pivoting
you are pivoting
he/she/it is pivoting
we are pivoting
you are pivoting
they are pivoting

Present Perfect
I have pivoted
you have pivoted
he/she/it has pivoted
we have pivoted
you have pivoted
they have pivoted

Past Continuous
I was pivoting
you were pivoting
he/she/it was pivoting
we were pivoting
you were pivoting
they were pivoting

Past Perfect
I had pivoted
you had pivoted
he/she/it had pivoted
we had pivoted
you had pivoted
they had pivoted

Future
I will pivot
you will pivot
he/she/it will pivot
we will pivot
you will pivot
they will pivot

Future Perfect
I will have pivoted
you will have pivoted
he/she/it will have pivoted
we will have pivoted
you will have pivoted
they will have pivoted

Future Continuous
I will be pivoting
you will be pivoting
he/she/it will be pivoting
we will be pivoting
you will be pivoting
they will be pivoting

Present Perfect Continuous
I have been pivoting
you have been pivoting
he/she/it has been pivoting
we have been pivoting
you have been pivoting
they have been pivoting

Future Perfect Continuous
I will have been pivoting
you will have been pivoting
he/she/it will have been pivoting
we will have been pivoting
you will have been pivoting
they will have been pivoting

Past Perfect Continuous
I had been pivoting
you had been pivoting
he/she/it had been pivoting
we had been pivoting
you had been pivoting
they had been pivoting

Conditional
I would pivot
you would pivot
he/she/it would pivot
we would pivot
you would pivot
they would pivot

Past Conditional
I would have pivoted
you would have pivoted
he/she/it would have pivoted
we would have pivoted
you would have pivoted
they would have pivoted

Collins English Verb Tables © HarperCollins Publishers 2011

Noun	1.	pivot - the person in a rank around whom the others wheel and maneuver parader, marcher - walks with regular or stately step
2.	pivot - axis consisting of a short shaft that supports something that turns axis of rotation, axis - the center around which something rotates pintle - a pin or bolt forming the pivot of a hinge
3.	pivot - the act of turning on (or as if on) a pivot; 'the golfer went to the driving range to practice his pivot' rotary motion, rotation - the act of rotating as if on an axis; 'the rotation of the dancer kept time with the music'
Verb	1.	pivot - turn on a pivot turn - change orientation or direction, also in the abstract sense; 'Turn towards me'; 'The mugger turned and fled before I could see his face'; 'She turned from herself and learned to listen to others' needs' pirouette - do a pirouette, usually as part of a dance

pivot

noun

1.hub, centre, heart, hinge, focal point, kingpinA large group of watercolours forms the pivot of the exhibition.

2.axis, swivel, axle, spindle, fulcrumThe pedal had sheared off at the pivot.

verb

1.turn, spin, revolve, rotate, swivel, twirlThe boat pivoted on its central axis.

pivot on somethingrely on, depend on, hang on, hinge on, be contingent on, revolve roundthe economic problems that pivoted on overseas trade

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Collins Thesaurus of the English Language – Complete and Unabridged 2nd Edition. 2002 © HarperCollins Publishers 1995, 2002

pivot

verb

1. To turn or cause to turn in place, as on a hinge or fixed point, tracing an arclike path:

2. To move, as a gun, laterally:

3. To change the direction or course of:

avert, deflect, deviate, divert, shift, swing, turn, veer.

čeposaotáčet se

fordulforgócsapmegfordul

pivoteren

pivot

[ˈpɪvət]

A.N (Mil, Tech) → pivotem (fig) → ejem (central)
she is the pivot around which the community revolves → ella es el eje sobre el quegira toda la comunidad

B.VT (= mount on pivot) → montar sobre un pivote; (= cause to turn) → hacer girar
he pivoted it on his hand → lo hizogirar sobre la mano

C.VI → girar (on sobre) she pivoted in front of the mirror → se dio una vueltafrente al espejo
to pivot on sth (fig) → giraralrededor de algo, depender de algo

Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

pivot

[ˈpɪvət]n

(fig) → pivotm
Their daughter was the pivot around which their lives revolved → Leur fille était le pivotautour duquel leurs viesgravitaient.

vi (= turn) → pivotervt fus (= depend on) → reposer sur

pivot

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vb: pret, ptp <pivoted>

n → Lagerzapfenm, → Drehzapfenm; (Mil) → Flügelmannm; (fig) → Dreh- und Angelpunktm; pivot bearing → Zapfenlagernt

vt → ; he pivoted it on his hand → er ließ es auf seiner Handkreiseln

vi → sich drehen; to pivot on something(fig) → sich um etwdrehen

pivot

pivot bridge

pivot tooth

Collins German Dictionary – Complete and Unabridged 7th Edition 2005. © William Collins Sons & Co. Ltd. 1980 © HarperCollins Publishers 1991, 1997, 1999, 2004, 2005, 2007

pivot

[ˈpɪvət]

2.vt → imperniare

pivot

(ˈpivət) noun

the pin or centre on which anything balances and turns. spil مِحْوَر، مُرْتَكَز، مَدار مِحْوَر الباب опорна точка eixo čep, osa der Drehpunkt akse άξονας περιστροφής eje pöördetelg محور napa pivotציר केन्द्र बिन्दु stožer, ključna točka forgócsap pusat völtur; þungamiðja, miðdepill cardine, 旋回軸 회전축 ašis ass; centrs pangsi spilomdreiningsakse, dreietappoś چورليځ، محور eixo pivot ось, центр вращения čap, os os stožer pivå, svängaxel เดือย mil, eksen 樞軸 точка опори; стрижень محور، مدار trục đứng 枢轴

verb – past tense, past participle ˈpivoted –

(with on) to turn (on). The door pivoted on a central hinge. draai يَدورُ على въртя се girar otáčet se sich drehen svinge στρέφομαιpivotar, girar sobre su eje pöörlema چرخیدن kääntyä pivoter לְהִסתוֹבֵב עַל צִירו घूमना opskrbiti stožerom, vrtjeti se oko nečega (meg)fordul vmin berputar snúast um/á girare 旋回する 회전하다 suktis griezties (ap kaut ko) memangsikan om een spil draaiendreie, svingeobracać się چور ليدل ، تاويدل rodar a pivota вращаться otáčať sa vrteti se okrog vrteti se oko pivotera, svänga, hänga หมุนรอบเดือย dönmek 在樞軸上轉動 крутитися, обертатися مدار پر گھومنا xoay quanh trục 在枢轴上转动

piv·ot

n. pivote, eje, parte que sostiene la corona de un diente.

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