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Topic: Fixed point

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Fixed point (mathematics)

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	point fixed glass
		Glazing fixing to the wall or many panels' junction in height are to be made by suitable stainless steel or steelcoated fittings, always provided with proper shock resistant gaskets.
		Cables are fixed to the ceiling and to the floor by proper stay rods, so to have the right cable tension like being unique.
		Spiders are fixed on the turnbuckle itself by proper bolts.
	www.faraone.it /infissi/point-fixed-glass.htm (267 words)

	NationMaster - Encyclopedia: Fixed point (Site not responding. Last check: 2007-10-07)
		In physics, a fixed point usually describes a quantum field theory or a critical behavior of a model of statistical mechanics that is invariant under the change of distance scales used by the renormalization group.
		The integer square root of a fixed point number divided by the square root of 2 to the F power where F is the number of bits of fraction in the fixed point number is the square root of the original fixed point number.
		Fixed points are of interest in themselves but they also provide a way to establish the existence of a solution to a set of equations.
	www.nationmaster.com /encyclopedia/Fixed-point (382 words)

	Doing It Fast, fixed point arithmetic techniques and fast 3d transforms
		Fixed point arithmetic uses ordinary integer operations to do arithmetic with numbers that have both a whole part and a fractional part.
		In the 2.2 fixed point we've been using for our examples 1 is 01.00 which is really the integer 100 or 1 with 2 zeros tacked on the end.
		To divide a fixed point by a fixed point you have to tack on even more zeros to the end of the number you are dividing.
	www.gameprogrammer.com /4-fixed.html (4813 words)

	PlanetMath: hyperbolic fixed point (Site not responding. Last check: 2007-10-07)
		If the dimension of the stable manifold of a fixed point is zero, the point is called a source; if the dimension of its unstable manifold is zero, it is called a sink; and if both the stable and unstable manifold have nonzero dimension, it is called a saddle.
		Cross-references: stable, point, stable manifold, dimension, iterate, least period, periodic point, linear hyperbolic isomorphism, diffeomorphism, fixed point, smooth manifold
		This is version 3 of hyperbolic fixed point, born on 2003-07-27, modified 2003-07-29.
	planetmath.org /encyclopedia/HyperbolicFixedPoint.html (149 words)

	Fixed Point Theorems
		A line is drawn from A to B and continued until it intersects the boundary of the disk at point C. Now the mapping under consideration is the mapping of A to C. This would be a continuous mapping of the interior onto the boundary.
		Some fixed points theorems can be stated in the form that the number of fixed points must be an odd number.
		However the tangential fixed point should be counted as a double fixed point, two fixed points in one.
	www.applet-magic.com /fixed.htm (1700 words)

	PlanetMath: Brouwer fixed point theorem (Site not responding. Last check: 2007-10-07)
		has the single fixed point at 0; dropping it from the domain yields a map with no fixed points.
		Cross-references: boundary, open, domain, map, interior, point, triangle, square, homeomorphic, fixed point, continuous function, unit ball, closed
		This is version 3 of Brouwer fixed point theorem, born on 2002-06-05, modified 2003-09-05.
	www.planetmath.org /encyclopedia/BrouwerFixedPointTheorem.html (166 words)

	FIXED POINT - Definition (Site not responding. Last check: 2007-10-07)
		The fixed point of a function, f is any value, x for which f x = x.
		The fixed point combinator, written as either "fix" or "Y" will return the fixed point of a function.
		Apart from that, fixed-point representation has the advantage of having uniform density, i.e., the smallest resolvable difference of the representation is B throughout the representable range, in sharp contrast to floating-point representations.
	www.hyperdictionary.com /dictionary/fixed+point (133 words)

	PlanetMath: Banach fixed point theorem (Site not responding. Last check: 2007-10-07)
		Theorem 1 (Banach Fixed Point Theorem) Every contraction has a unique fixed point.
		There is an estimate to this fixed point that can be useful in applications.
		This is version 17 of Banach fixed point theorem, born on 2002-03-07, modified 2004-02-09.
	www.planetmath.org /encyclopedia/BanachFixedPointTheorem.html (286 words)

	Brouwer fixed point theorem Summary
		Because the properties involved (continuity, being a fixed point) are invariant under homeomorphisms, the theorem equally applies if the domain is not the closed unit ball itself but some set homeomorphic to it (and therefore also closed, bounded, connected, without holes, etcetera).
		The Brouwer fixed point theorem was one of the early achievements of algebraic topology, and is the basis of more general fixed point theorems which are important in functional analysis.
		This is equivalent to the Brouwer fixed point theorem for dimension 2.
	www.bookrags.com /Brouwer_fixed_point_theorem (2012 words)

	fixed point as a type - GameDev.Net Discussion Forums
		I Implimented an entire fixed point class a year or two ago, and it turned out to be slower than standard floating point math.
		By the time you push 2 opperands on the stack, do your "fast" fixed point calculation (which is little if any faster than floating point anyhow), and return the results, floating point has already passed you up and is now taking a leisurely nap in the sun.
		At that point you may just say to hell with it, lets do everything with integers (which may not be a bad idea), but fixed point is a viable option.
	www.gamedev.net /community/forums/topic.asp?topic_id=379830 (1288 words)

	Ada 95 RM - 3.5.10 Operations of Fixed Point Types
		Small may be specified for nonderived fixed point types via an attribute_definition_clause (see 13.3); the expression of such a clause shall be static.
		S'Aft yields the number of decimal digits needed after the decimal point to accommodate the delta of the subtype S, unless the delta of the subtype S is greater than 0.1, in which case the attribute yields the value one.
		S'Digits denotes the digits of the decimal fixed point subtype S, which corresponds to the number of decimal digits that are representable in objects of the subtype.
	www.csupomona.edu /reference/ada/rm95html-1.0/rm9x-03-05-10.html (580 words)

	Speex: A free codec for free speech
		This is a brown-paper-bag release fixing a pretty bad bug that affected the fixed-point port in 1.1.11.
		Fixed a potential bug (unconfirmed) that might cause a segfault in special circumstances.
		In this bugfix release: a fix for a multithreading bug and a correction for an underflow problem that could slow decoding dramatically on x86 processors.
	www.speex.org /news (801 words)

	IntroductionToFixedPointMath - bookofhook - Trac (Site not responding. Last check: 2007-10-07)
		As the name implies, a fixed point number places the "decimal" point between the whole and fractional parts of a number at a fixed location, providing f bits of fractional precision.
		Fixed point multiplication is a bit uglier, but not too bad -- multiply the two numbers, then shift down by some number of bits to get back into the output format you want.
		Fixed point is a wonderful way to get around the limitations of systems with slow (or non-existent) floating point units.
	trac.bookofhook.com /bookofhook/trac.cgi/wiki/IntroductionToFixedPointMath (3271 words)

	Ada 95 RM - G.2.3 Model of Fixed Point Arithmetic
		For a fixed point multiplication or division whose (exact) mathematical result is v, and for the conversion of a value v to a fixed point type, the perfect result set and close result set are defined as follows:
		A multiplication P * Q of an operand of a fixed point type F by an operand of an integer type I, or vice-versa, and a division P / Q of an operand of a fixed point type F by an operand of an integer type I, are also allowed.
		The possibility of overflow in the result of a predefined arithmetic operation or conversion yielding a result of a fixed point type T is analogous to that for floating point types, except for being related to the base range instead of the safe range.
	www.csupomona.edu /reference/ada/rm95html-1.0/rm9x-G-02-03.html (973 words)

	Fixed Point Math (Site not responding. Last check: 2007-10-07)
		The idea behind fixed point math is that we pretend that there is a decimal point.
		Addition and subtraction work are basically the same with fixed point numbers are they do with integer or floats.
		Fixed point math is something that has applications in many, many areas of computer graphics.
	members.aol.com /form1/fixed.htm (461 words)

	The Brouwer-Kakutani Fixed Point Theorem
		That is, self-replicating molecules are an instantiation of the Fixed Point Theorem where the map is the one determined by the laws of Physics and Chemistry.
		Evolution is evidently the process of moving to ever stabler fixed points, working against the force of Entropy (the destroyer) which leads back to decay and disorder.
		Nevertheless, such a Fixed Point does seem to be a point of attraction of the Advance of Civilization, so the best way for an individual to lead society in that direction is by setting an example that is worthy of imitation.
	underground.musenet.org:8080 /utnebury/fixed.point.html (1029 words)

	Fixed Point Theory and Applications
		We approximate the common fixed points of a finite family of nonexpansive nonself-mappings by weak and strong convergence of the scheme in a uniformly convex Banach space.
		This paper concerns a formula which relates the Lefschetz number L(f) for a map f:Mand#x2192;Mand#x2032; to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of and#x2202;M. Here M is a compact manifold and Mand#x2032; is M with a collar attached.
		Using retraction mapping and fixed point method, we study the existence of solution of general quasi-variational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem.
	www.emis.de /journals/HOA/FPTA/323d.xml?journal=FPTA (2171 words)

	Brouwer
		One of the major contributors to fixed point theory was L E J Brouwer.
		Recently, in the comparison of fixed points of different mappings where the mappings are ordered and increasing for a certain order >=, it has been shown that every fixed point of a lower (higher) mapping has at least one higher (lower) fixed point in a higher (lower) mapping.
		Not coincidentally at this point, we raise to your consciousness that the flow lines of the winds on the earth's surface constitute a continuous mapping of that surface to another point thereon.
	hypatia.math.uri.edu /~kulenm/mth381pr/fixedpoint/fixedpoint.html (1661 words)

	Model of Fixed Point Arithmetic
		For decimal fixed point types, the attribute T'Round may be used to imply explicit conversion with rounding (see 3.5.10).
		A multiplication P * Q of an operand of a fixed point type F by an operand of an integer type I, or vice-versa, and a division P / Q of an operand of a fixed point type F by an operand of an integer type I, are also allowed.
		The possibility of overflow in the result of a predefined arithmetic operation or conversion yielding a result of a fixed point type T is analogous to that for floating point types, except for being related to the base range instead of the safe range.
	www.adapower.com /rm95/RM-G-2-3.html (958 words)

	PlanetMath: fixed point (Site not responding. Last check: 2007-10-07)
		, is a point that remains constant upon application of that function, i.e.:
		See Also: Banach fixed point theorem, Brouwer fixed point theorem, Schauder fixed point theorem, fixed point property, Tarski-Knaster theorem
		This is version 6 of fixed point, born on 2002-03-08, modified 2006-09-15.
	planetmath.org /encyclopedia/FixedPoint.html (60 words)

	Programmable Logic DesignLine \| Fixed-point DSP and algorithm implementation
		The differences between fixed and floating point processors are significant enough that they require very different internal implementation, instruction sets and approaches for algorithm implementation.
		The typically lower cost and higher speed of fixed point DSP implementations are traded off against added design effort for algorithm implementation analysis, and data and coefficient scaling to avoid accumulator overflow.
		The output of the ADC is a stream of sampled fixed word length values which represent the analog input signal at the discrete sample points determined by the ADC's sampling frequency.
	www.pldesignline.com /193402803?cid=RSSfeed_programmablelogicdesignline_pldlRSS (1131 words)

	Dr. Dobb's \| Fixed-Point DSP and Algorithm Implementation \| October 25, 2006
		The differences between fixed and floating point processors are significant enough that they require very different internal implementation, instruction sets and approaches for algorithm implementation.
		The typically lower cost and higher speed of fixed point DSP implementations are traded off against added design effort for algorithm implementation analysis, and data and coefficient scaling to avoid accumulator overflow.
		The output of the ADC is a stream of sampled fixed word length values which represent the analog input signal at the discrete sample points determined by the ADC's sampling frequency.
	www.ddj.com /dept/embedded/193402256 (990 words)

	Introduction to DSP - DSP processors: data formats
		The size of the fraction represented by the smallest bit is the precision of the fixed point format.
		If a fixed point number becomes too large for the available word length, the programmer has to scale the number down, by shifting it to the right: in the process lower bits may drop off the end and be lost
		If a fixed point number is small, the number of bits actually used to represent it is small.
	www.bores.com /courses/intro/chips/6_data.htm (636 words)

	Fixed Point Combinator (Site not responding. Last check: 2007-10-07)
		A fixed point is a point in a function's domain which is equal to the corresponding point in its range.
		A fixed point of f is an x in A that equals f(x).
		The fixed point combinator is a HigherOrderFunction which returns a fixed point of its argument.
	c2.com /cgi/wiki?FixedPointCombinator (340 words)

	Fixed-Point Theorems
		Working on the theory of games, John Nash (1950) was among the first to use Kakutani's Fixed Point Theorem.
		, thus point d is not a fixed point.
		Obviously, we have a fixed-point at point the intersection of the correspondence with the 45
	cepa.newschool.edu /het/essays/math/fixedpoint.htm (544 words)

	IEEE Standard 754 Floating-Point (Site not responding. Last check: 2007-10-07)
		Fixed point places a radix point somewhere in the middle of the digits, and is equivalent to using integers that represent portions of some unit.
		The range of positive floating point numbers can be split into normalized numbers (which preserve the full precision of the mantissa), and denormalized numbers (discussed later) which use only a portion of the fractions's precision.
		Since the sign of floating point numbers is given by a special leading bit, the range for negative numbers is given by the negation of the above values.
	steve.hollasch.net /cgindex/coding/ieeefloat.html (1366 words)

	Fixed Point Theorems/Reflection Conditions
		Infinite-dismantlability also gives an algorithmic insight into a classical result about the fixed point property for ordered sets of height 1 (recall that the height of an ordered set P is the number of elements in the largest chain in P minus 1):
		Thus if every endomorphism of G has a fixed vertex or a fixed edge, then every order-preserving map of P that maps minimal elements to minimal elements has a fixed point and consequently P has the fixed point property.
		However by Theorem 3.21 P has the fixed point property iff P is connected and has no crowns and no infinite fences.
	www.csi.uottawa.ca /ordal/papers/schroder/node13.html (634 words)

	Fixed Point Constraints
		The basic idea of the transformation used is that it may often be possible to identify one or more points within the image that the user wishes to be definitely visible and thereby reduce the search space to setting the viewing angles.
		If one point is fixed then there are two degrees of freedom left to set the view and if there are two fixed points then there is only one degree of freedom.
		In the 3D paint program the fixed point constraints are implemented so that they remain in force whilst only the angles are being modified.
	genex.hgu.mrc.ac.uk /Software/paint/paint/node10.html (309 words)

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