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Topic: Bilinear

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bilinear operator

bilinear form

Bilinear interpolation

bilinear transformation

bilinear filtering

singular bilinear form

bilinear product

Hodge Riemann bilinear relations

non degenerate bilinear form

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	Citations: Approximation procedures for the optimal control of bilinear and nonlinear systems - Cebuhar, Costanza ...
		In [6] a finite time optimal control of singularly perturbed bilinear systems is derived with a....
		Another 2 variation on the nonlinear control problem is an uncertain system, where unknown parameters are involved in the equation, as discussed in [27, 28] A method dealing only with systems where the number of state and control variables are the same is presented in [29] In this paper a....
		In the bilinear control problem is reduced to a sequence of linear control problems that converge uniformly to the optimal bilinear control.
	citeseer.ist.psu.edu /context/100293/0 (650 words)

	Bilinear operator - Wikipedia, the free encyclopedia
		In mathematics, a bilinear operator is a generalized "multiplication" which satisfies the distributive law.
		The set L(V,W;X)of all bilinear maps is a linear subspace of the space (viz vector space, module) of all maps from V×W into X.
		In general, for a vector space V over a field F, a bilinear form on V is the same as a bilinear operator V × V → F.
	en.wikipedia.org /wiki/Bilinear_operator (634 words)

	PlanetMath: bilinear form
		We note that for a real positive-definite bilinear form that every subspace is non-degenerate, so this gives the usual result about inner product spaces.
		An inner product space on a vector space is a bilinear form if its field is real, but not if it is complex.
		This is version 41 of bilinear form, born on 2002-01-24, modified 2005-01-08.
	planetmath.org /encyclopedia/BilinearForm.html (367 words)

	PlanetMath: skew-symmetric bilinear form
		A skew-symmetric (or antisymmetric) bilinear form is a special case of a bilinear form
		A bilinear form is skew-symmetric iff its representing matrix is skew-symmetric.
		This is version 4 of skew-symmetric bilinear form, born on 2002-11-28, modified 2005-05-08.
	planetmath.org /encyclopedia/Antisymmetric2.html (171 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		A bilinear flow period, which is controlled by reservoir heterogeneity, is well known, but this type of flow may also appear in homogeneous reservoirs.
		Bilinear flow may occur for a long horizontal well or vertical fracture of high conductivity (uniform flux or infinite conductivity).
		The controlling factors for the existence of the bilinear flow period are length of the well and the directional permeabilities.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=136994 (265 words)

	bilinear interpolation Definition: TechEncyclopedia from TechWeb
		A texture mapping technique that produces a reasonably realistic image, also known as "bilinear filtering" and "bilinear texture mapping." An algorithm is used to map a screen pixel location to a corresponding point on the texture map.
		A weighted average of the attributes (color, alpha, etc.) of the four surrounding texels is computed and applied to the screen pixel.
		The term bilinear refers to the performing of interpolations in two dimensions (horizontal and vertical).
	www.techweb.com /encyclopedia/defineterm.jhtml?term=bilinearinterpolation (427 words)

	Bilinear Transformation
		The bilinear transform is defined by the substitution
		Note that at most one resonant frequency can be preserved under the bilinear transformation of a mass-spring-dashpot system.
		In particular, ``equal ripple'' is preserved for optimal filters of the elliptic and Chebyshev types because the values taken on by the frequency response are identical in both cases; only the frequency axis is warped.
	ccrma-www.stanford.edu /~jos/lumped/Bilinear_Transformation.html (272 words)

	3DCenter - Will "brilinear" filtering persist?
		Bilinear filtering means to mix 4 texel from the "most suitable" MIP map to one color value.
		The LOD formula provides altogether the highest possible sharpness degree, which is evenly achievable with bilinear filter.
		Bilinear filtering causes hard bands at the point where different detail resolutions adjoin.
	www.3dcenter.org /artikel/2003/10-26_a_english.php (1450 words)

	CoolTechZone::Bilinear, Trilinear, and MIP Mapping Technologies Explained (Site not responding. Last check: 2007-10-26)
		Bilinear Filtering (or interpolation) is the effect you take from four nearby pixels of the surrounding texture map—these are called “texels”—and you average between them in order to remove the roughness and create a gradual change, thus making a smooth image.
		Bilinear filtering does this when the resolution is resized and the image becomes distorted.
		Bilinear filtering may be better noticed if you zoom in on the ground below and compare a segment of the ground with bilinear filtering and without it; thus, as you can see, bilinear filtering basically produces the anti-aliasing effect.
	www.cooltechzone.com /index.php?option=content&task=view&id=454&Itemid=0&limit=1&limitstart=1 (280 words)

	bilinear :: Functions (Signal Processing Toolbox)
		The bilinear transformation is a mathematical mapping of variables.
		In prewarped mode, the bilinear transformation maps the s-plane into the z-plane with
		It adds extra zeros at -1 so the resulting system has equivalent numerator and denominator order.
	www.mathworks.com /access/helpdesk/help/toolbox/signal/bilinear.html (366 words)

	THE BILINEAR TRANSFORM (Site not responding. Last check: 2007-10-26)
		By inspection of Figures 20 and 21, it is found that the bilinear approximation (42) or (43) also maps the exterior of the unit circle into the lower half-plane.
		Thus, although the bilinear approximation is an approximation, it turns out to exactly preserve the minimum-phase property.
		Clearly, the folding theorem is too generous for applications involving the bilinear transform.
	sepwww.stanford.edu /sep/prof/fgdp/c2/paper_html/node9.html (450 words)

	Writing Systems and Manuscripts
		Bilinear scripts and fonts fill the entire space between the upper and lower limits.
		Because they fill the writing zone, bilinear scripts are tightly constrained on the horizontal plane and cannot move on the vertical plane at all (Figure 1).
		Proportional scripts (and fonts), bilinear, trilinear, or quattrolinear, are designed relative to the width of the minim and the symbol 'o'.
	www.st-andrews.ac.uk /~www_sd/altman_writing.html (8789 words)

	Vision Engineer - Bilinear Filtering (Site not responding. Last check: 2007-10-26)
		Bilinear filtering or interpolation is used in computer graphics to reduce "blockiness".
		Bilinear filtering solves "blockiness" by taking 4 neighbouring pixels of the texture map [texels], and averaging between them.
		However, since bilinear filtering samples neighbouring pixels from a square area, it can only produce convincing results for surfaces at a right angle to the viewer.
	www.visionengineer.com /comp/bilinear_filtering.shtml (206 words)

	bilinear (Site not responding. Last check: 2007-10-26)
		Theory: Given a piecewise flat filter design, you can transform it from the s-plane to the z-plane while maintaining the band edges by means of the bilinear transform.
		This is significant since the bilinear transform creates numerous extra poles and zeros, most of which cancel.
		Those which do not cancel have a "fill-in" effect, extending the shorter of the sets to have the same number of as the longer of the sets of poles and zeros (or at least split the difference in the case of the band pass filter).
	octave.sourceforge.net /index/f/bilinear.html (263 words)

	The Bilinear Transform
		The formula for a general first-order (bilinear) conformal mapping of functions of a complex variable is conveniently expressed by [
		Bilinear transformations map circles and lines into circles and lines (lines being viewed as circles passing through the point at infinity).
		``The Bark and ERB Bilinear Transforms'', by Julius O. Smith III and Jonathan S. Abel, preprint of version accepted for publication in the IEEE Transactions on Speech and Audio Processing, December, 1999.
	ccrma.stanford.edu /~jos/bbt/Bilinear_Transform.html (191 words)

	[music-dsp] Bilinear Transform (Site not responding. Last check: 2007-10-26)
		If you mean the impulse invariance method of filter design, it is not usually used because it is more difficult to compute than the bilinear transform and the frequency response will alias.
		Higher order versions of the bilinear transform (s = A(z)/B(z), A, B polynomials) are not used because either stability is not preserved or the mapping of the frequency axis to the unit circle is not 1 to 1.
		Pre-warping basically means choosing your cutoff frequency or other characteristic frequencies in the z domain, transferring them to the s domain using one direction of the bilinear transform, using them in your filter formulas to design your s domain filter, then transforming that back to the z-domain.
	shoko.calarts.edu /pipermail/music-dsp/2000-May/004348.html (504 words)

	A Novel Approach to Real-time Bilinear Interpolation (Site not responding. Last check: 2007-10-26)
		Bilinear interpolation is often used to improve image quality after performing spatial transformation operations such as digital zooming or rotation.
		In the traditional case where the input coordinates appear in a raster-based fashion, the required pixel values can be obtained from the previous calculation, the frame buffer and a single line cache.
		This paper presents a novel approach to performing real-time bilinear interpolation that is useful in applications such as lens distortion correction where the input coordinates follow a curved path that spans multiple rows.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/delta/2004/2081/00/2081toc.xml&DOI=10.1109/DELTA.2004.10055 (237 words)

	3D Chipset Specs
		The Radeon 7xxx series cannot do trilinear and anisotropic filtering at the same time; it reverts to bilinear when anisotropic filtering is enabled.
		Early drivers on the Radeon 8500 used to use some flavor of dual bilinear instead of trilinear filtering.
		And they do bilinear filtering instead of trilinear when aniso is enabled.
	users.rcn.com /chare/video.htm (1104 words)

	GameDev.net - Bilinear Interpolation Of Texture Maps
		Bilinear interpolation (now on called 'bilerp' for short) is a process of filtering the surrounding texels, to smooth out any jaggies occuring between pixels, and giving the screen a smoother look.
		I actually tried approximating bilinear texturing in direct RGB mode by using a table.
		Now that you have all this information, you can implement a bilinear texturing system.
	www.gamedev.net /reference/articles/article810.asp (936 words)

	NV40 anisotropic filtering investigation - nV News Forums
		Bilinear Texture Filtering: Bilinear filtering is a computationally cheap but low quality texture filtering.
		Trilinear Texture Filtering: Trilinear filtering is a high quality bilinear filter which uses the four closest pixels in the second most suitable mip map to produce smoother transitions between mip map levels.
		This mode is pretty much pure bilinear with texture stage optimizations enabled, With texture optimizations disabled there appears to alot of quasi trilinear filtering occuring.
	www.nvnews.net /vbulletin/showthread.php?t=31535 (1600 words)

	Digital Filter Solutions
		None of the techniques are perfect, but in general the Bilinear transformation maps the entire frequency response of the desired filter, the Impulse Invariant transformation preserves the impulse time response, and the Step Invariant preserves the step time response.
		In the case of the Bilinear transformation, the entire continuous frequency spectrum is mapped to the discrete unit circle.
		When digitized with a Bilinear transformation, and sampled at 25Hz, the frequency response exhibits aliasing errors as shown.
	www.filter-solutions.com /digital.html (1554 words)

	Citebase - Bilinear R-Parity Violation
		We review some of the main features of Bilinear R-Parity Violation (BRpV), defined by a quadratic term in the superpotential which mixes lepton and Higgs superfields and is proportional to a mass parameter epsilon.
		We show that the minimal R-parity breaking model characterized by an effective bilinear violation of R-parity in the superpotential is consistent with minimal N=1 supergravity unification with radiative breaking of the electroweak symmetry and universal scalar and gaugino masses.
		We investigate a supersymmetric scenario where R-parity is explicitly broken through a term bilinear in the lepton and Higgs superfields in the superpotential.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-ph/9802407 (1136 words)

	www.phdcomics.com :: View topic - Bilinear models
		this is a long shot...would anyone care to attempt to explain bilinear models (to an engineer, mind you.
		Bilinear means linear in each input, if you hold the other input constant.
		its just i was going through some stuff for my thesis, and kept stumbling across bilinear models.
	www.phdcomics.com /proceedings/viewtopic.php?t=1163&view=previous (489 words)

	Bilinear Covariants
		The wave functions themselves do not represent observables directly, but one can construct bilinear experessions of the wave functions which have the transformation properties of tensors.
		different bilinears have their own distinct transformation properties.
		In particle physics theories of the weak interaction, and the less established theories involving gravity and super-symmetry, a rich set of bilinear forms are used.
	www.phys.ualberta.ca /~gingrich/phys512/latex2html2/node56.html (191 words)

	The Chronicle: 4/25/2003: Every Unhappy Family Has Its Own Bilinear Influence Function (Site not responding. Last check: 2007-10-26)
		They used these to develop bilinear influence functions, which describe a person's ability to affect his or her spouse's mood.
		Repair attempts typically include jokes, soothing comments, or changes of subject; damping generally involves making hurtful comments even when one's partner is clearly trying to be positive.
		"Without repair and damping, we knew that the bilinear influence functions weren't going to work," says Kristin Swanson, "because the equations allowed people to just spontaneously combust with happiness or spontaneously combust with unhappiness.
	www.chronicle.com /free/v49/i33/33a01401.htm (2418 words)

	Ray Bilinear Patch Intersections (Site not responding. Last check: 2007-10-26)
		The object to intersect is typically a sphere, triangle, or polygon but many surface types are possible.
		In this work we consider intersections between rays and the simplest parametric surface, the bilinear patch.
		The ray bilinear patch intersection software is "Open Source" according to the MIT License located at:
	albert.washcoll.edu /~sramsey2/research/bp (128 words)

	J. Hietarinta: Work on solitons
		Hietarinta, A. Ramani and B. Grammaticos: Continuous vacua in bilinear soliton equations, J. Phys.
		Hietarinta: A search of bilinear equations passing Hirota's three-soliton condition: I. KdV-type bilinear equations, J.
		Hietarinta: Gauge symmetry and the generalization of Hirota's bilinear method, J. Nonlin.
	users.utu.fi /hietarin/solitons.html (645 words)

	Indiegamer Developer Discussion Boards - Bilinear Resample (Site not responding. Last check: 2007-10-26)
		Unlike bilinear or bicubic it uses all available information from the source image to create a high quality result.
		For example, if you resize by a factor of 4 then each pixel in the result image will be calculated from a 4 by 4 box of pixels in the original image.
		Bilinear resampling down involves blurring as well - you lose a lot of detail.
	forums.indiegamer.com /archive/index.php/t-940.html (805 words)

	PID controller with Bilinear Approximation (Site not responding. Last check: 2007-10-26)
		The bilinear transformation is another method which maps the entire left half of the s-plne into the unit circle in the z-plane.
		To map to the z-plane we substitute the bilinear relation into the above PID transfer function, so the discrete-time PID controller becomes.
		For bilinear approximation to derivative, the "tustin" method must be used.
	www.engin.umich.edu /group/ctm/extras/PID_Bilinear.html (276 words)

	Physics at Minnesota:
		The bilinear transformation is a mathematical mapping of variables.
		The bilinear transformation maps the s-plane into the z-plane by
		In prewarped mode, the bilinear transformation maps the s-plane into the z-plane with
	www.physics.umn.edu /support/doc/matlab/toolbox/signal/bilinear.html (379 words)

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