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| | Content of the AAA_readme file at ftp.cs.wisc.edu/Approx |
 | | Items on: approximation orders, box splines and exponential box splines, dimensions of kernels of linear operators, frames, multivariate polynomial interpolation, polynomial ideals, commutative algebra and approximation theory, quasi-interpolation, radial basis function approximation, refinable functions, scattered data approximation, shift-invariant spaces, subdivision, surveys, univariate splines, wavelets, Weyl-Heisenberg systems, linear algebra, \TeX, splinebib, file mailing,... | | | Approximation orders of and approximation maps from local principal shift-invariant spaces | | | Approximation in $L_p(\Rd)$ from spaces spanned by the perturbed integer translates of a radial basis function |
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http://www.cs.wisc.edu/~deboor/ftpreadme.html
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| | Content of the AAA_readme file at ftp.cs.wisc.edu/Approx |
| | Items on: approximation orders, box splines and exponential box splines, dimensions of kernels of linear operators, frames, multivariate polynomial interpolation, polynomial ideals, commutative algebra and approximation theory, quasi-interpolation, radial basis function approximation, refinable functions, scattered data approximation, shift-invariant spaces, subdivision, surveys, univariate splines, wavelets, Weyl-Heisenberg systems, linear algebra, \TeX, splinebib, file mailing,... | | | Approximation in $L_p(\Rd)$ from spaces spanned by the perturbed integer translates of a radial basis function | | | On multivariate approximation by integer translates of a basis function |
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http://www.cs.wisc.edu/~deboor/ftpreadme.html
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| | Division of Approximation Theory: list of publications |
| | Janik, On approximation of analytic functions and generalized orders, Proceedings of the Tenth Conference on Analytic Functions (Szczyrk, 1990). | | | Paw³ucki, W. Ple¶niak, Approximation and extension of $C\sp \infty$ functions defined on compact subsets of Cn, Deformations of mathematical structures (Lód?/Lublin, 1985/87), 283--295, Kluwer Acad. | | | Paw³ucki, W. Ple¶niak, Approximation and extension of $C\sp \infty$ functions defined on compact subsets of Cn, Deformations of mathematical structures (\Lód?/Lublin, 1985/87), 283--295, Kluwer Acad. |
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http://www.im.uj.edu.pl/institute/chairs/publications/kta
(1598 words)
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| | Content of the AAA_readme file at ftp.cs.wisc.edu/Approx |
| | Items on: approximation orders, box splines and exponential box splines, dimensions of kernels of linear operators, frames, multivariate polynomial interpolation, polynomial ideals, commutative algebra and approximation theory, quasi-interpolation, radial basis function approximation, refinable functions, scattered data approximation, shift-invariant spaces, subdivision, surveys, univariate splines, wavelets, Weyl-Heisenberg systems, linear algebra, \TeX, splinebib, file mailing,... | | | Approximation in $L_p(\Rd)$ from spaces spanned by the perturbed integer translates of a radial basis function | | | On multivariate approximation by integer translates of a basis function |
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http://www.cs.wisc.edu/~deboor/ftpreadme.html
(1585 words)
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| | Orders |
| | Orders of approximation Often in order of magnitude of the rounding error involved. | | | Orders of magnitude (numbers) (), a googolplex, order of magnitude of an upper bound that occurred in a proof of Skewes... | | | Orders of magnitude (area) The pages linked in the right-hand column contain lists of areas that are of the same order o... |
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http://www.brainyencyclopedia.com/topics/orders.html
(347 words)
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| | Iske, Armin : Reconstruction of... |
| | The suggested method is shown to be well-posed, and moreover by using local error estimates from radial basis function interpolation, approximation orders for the least squares error are proven. | | | An efficient adaptive algorithm for the purpose of automatically selecting a suitable basis of the approximation space is provided. | | | Based on constrained least squares approximation and techniques from computational geometry, this paper shall provide a new approximation scheme which achieves to combine well-known features from radial basis function interpolation with recent developments concerning scattered data filtering. |
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http://pck3.ma.tum.de/veroeff/html/990.65001.html
(347 words)
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| | MOMS |
| | We provide the explicit form of the MOMS that maximize the approximation accuracy when the step-size is small enough. | | | We show that it is already substantial for small orders and that it further increases with the approximation order L. | | | Since the optimal functions are continuous, but not differentiable, for even orders, and even only piecewise continuous for odd orders, our result implies that regularity has little to do with approximating performance. |
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http://bigwww.epfl.ch/publications/blu0101.html
(347 words)
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| | Research Experience for Undergraduates |
| | Chebyshev Approximation on the Surface of the Unit Ball. | | | Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms. | | | On the Rate of Convergence of Discretization in Chebyshev Approximation |
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http://math.fullerton.edu/mathews/n2003/chebyshevpoly/ChebyshevPolyBib/Links/ChebyshevPolyBib_lnk_3.html
(483 words)
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| | Weierstrass Approximation Theorem |
| | This does not necessarily mean that a Taylor series expansion can be used to find such a polynomial since, in particular, the function must be differentiable of all orders throughout | | | The Weierstrass approximation theorem assures us that polynomial approximation can get arbitrarily close to any continuous function as the polynomial order is increased. | | | The main point here is that, thanks to the Weierstrass approximation theorem, we know that good polynomial approximations exist for any continuous function. |
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http://ccrma-www.stanford.edu/~jos/mdft/Weierstrass_Approximation_Theorem.html
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| | Class Average Distance |
| | Increasing dash length corresponds to increasing order of approximation. | | | As the order of approximation is increased, the typical average distance decreases significantly. | | | It is clear, however, average predictions tend to improve with increase in order of approximation. |
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http://www.santafe.edu/~hag/class/node29.html
(158 words)
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| | Wiley::Comparison Methods for Stochastic Models and Risks |
| | Stochastic orders are important approximation tools that provide valuable insight into the behaviour of complex stochastic models. | | | Research into stochastic orders is blossoming, with many open problems being studied and a wide range of applications explored. | | | Researchers and graduate students studying stochastic orders will find the comprehensive coverage of the subject ideal for their needs. |
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http://www.wiley.com/cda/product/0,,0471494461desc2740,00.html
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| | Weierstrass Approximation Theorem |
| | This does not necessarily mean that a Taylor series expansion can be used to find such a polynomial since, in particular, the function must be differentiable of all orders throughout | | | The Weierstrass approximation theorem assures us that polynomial approximation can get arbitrarily close to any continuous function as the polynomial order is increased. | | | Furthermore, there can be points, even in infinitely differentiable functions, about which a Taylor expansion will not yield a good approximation, as illustrated in the next section. |
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http://ccrma-www.stanford.edu/~jos/mdft/Weierstrass_Approximation_Theorem.html
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| | 97-145 |
| | Then we show that at any finite order the error of the WKB approximation measured in {\em the natural units of the mean energy level spacing} does not go to zero when the quantum number goes to infinity. | | | Therefore we make the general conclusion that the semiclassical approximations fail to predict the individual energy levels within a vanishing fraction of the mean energy level spacing. | | | For this system we show that any finite order WKB (semiclassical) approximation fails to predict the individual energy levels within a vanishing fraction of the mean energy level spacing. |
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http://www.ma.utexas.edu/mp_arc/html/papers/97-145
(1247 words)
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| | The factorisation approximation in electron-atom ionisation |
| | The distorted-wave impulse approximation for ionisation in a three-body model treats the two-body subsystems to all orders in the relevant potentials. | | | It can only be calculated by making the approximation of factorising out the electron-electron T matrix. | | | In the distorted-wave Born approximation the factorised and unfactorised amplitudes can both be calculated. |
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http://stacks.iop.org/0953-4075/22/2041
(1247 words)
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| | Atomic valences and bond orders for crystals in HF SCF theory |
| | The one determinant approximation means that a many-electron wave function of a system (molecule or crystal) is approximated by a single antisymmetrized product (determinant) of one-electron functions | | | In Section 2 the properties of the electron density operators for a one determinant wave function are considered for different approximations used in the SCF Hartree-Fock calculations of crystals. | | | In the ROHF approximation the same set of orbitals describes |
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http://wgc.chem.pu.ru/~valera/papers/Fock98
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| | Approximation Of Thermal Equilibrium For Quantum Gases With Discontinuous Potentials And Application To Semiconductor Devices - Gardner, Ringhofer (ResearchIndex) |
| | Gardner and C. Ringhofer, "Approximation of thermal equilibrium for quantum gases with discontinuous potentials and application to semiconductor devices," SIAM Journal on Applied Mathematics, accepted for publication, 1998. | | | This approximation can be used as initial data for transient solutions of the quantum Liouville equation, to derive quantum mechanical correction terms to the classical hydrodynamic model, or to construct an e#ective partition function... | | | Abstract:. We derive an approximate solution valid to all orders of h to the Bloch equation for quantum mechanical thermal equilibrium distribution functions via asymptotic analysis for high temperatures and small external potentials. |
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http://citeseer.ist.psu.edu/gardner98approximation.html
(566 words)
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| | Orders of magnitude - Wikipedia, the free encyclopedia |
| | Orders of magnitude are generally used to make very approximate comparisons. | | | An order of magnitude estimate is sometimes also called a zeroth order approximation. | | | If they differ by two orders of magnitude, they differ by a factor of about 100. |
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http://en.wikipedia.org/wiki/Order_of_magnitude
(566 words)
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| | DBLP: Svatopluk Poljak |
| | Charles Delorme, Svatopluk Poljak: Combinatorial Properties and the Complexity of a Max-cut Approximation. | | | Jørgen Bang-Jensen, Svatopluk Poljak: Eulerian trails through a set of terminals in specific, unique and all orders. | | | Peter Alles, Jaroslav Nesetril, Svatopluk Poljak: Extendability, Dimensions, and Diagrams of Cycle Orders. |
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http://www.vldb.org/dblp/db/indices/a-tree/p/Poljak:Svatopluk.html
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| | Pade.html |
| | We have conducted some preliminary investigations used SCALAPACK for the inversion and using a range of orders for the Pade' approximation. | | | In contrast to a truncated Taylor series, the Pade' approximations to the matrix exponential are orthogonal by construction. | | | The matrix approximation to EXP(K) employed in SCF minimizations should be accurately orthogonal as well as appropriately close to the exponential value. |
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http://www.emsl.pnl.gov/proj/tms/hpcc_actinides/research-98/argonne/Pade.html
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| | Pade.html |
| | We have conducted some preliminary investigations used SCALAPACK for the inversion and using a range of orders for the Pade' approximation. | | | The matrix approximation to EXP(K) employed in SCF minimizations should be accurately orthogonal as well as appropriately close to the exponential value. | | | The standard Taylor's series expansion uses powers of the K matrix whereas an alternative block-matrix representation of K and its powers exploits the symmetry that is present in the matrix EXP(K). |
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http://www.emsl.pnl.gov/proj/tms/hpcc_actinides/research-98/argonne/Pade.html
(479 words)
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| | w951233w.txt |
| | In its interim judgment order, the district court also considered HUD's request for disgorgement of petitioners' illegal profits, and found that HUD's proposed disgorgement figure of $8,648,048 was a "reasonable approximation" of the amount of profits petitioners received from their unlawful activities. | | | It noted that petitioners had been twice held in contempt by the magistrate judge for defying the court's orders, and had otherwise made it clear to the court that they did "not feel bound by the orders of this court (or by the law)." Id. at A33-A34. | | | This Court's jurisdiction is invoked under 28 U.S.C. Petitioner Cost Control Marketing and Sales Management of Virginia, Inc. (CCMV) is a Virginia corporation formed for the sole purpose of purchasing, marketing, and selling unimproved lots of land in Lake Monticello, Virginia, a subdivision of over 4,500 lots. |
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http://www.usdoj.gov/osg/briefs/1995/w951233w.txt
(3614 words)
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| | Amway: The Untold Story: Price Comparisons |
| | Most of the Amway products I selected are available from the RDCs, which means that their is a shipping cost of four percent of retail on orders over $100 and $4 on orders under $100 (our direct distributor always charged us shipping charges based on that--others distributors may have been charged less, or more). | | | These percentages give the cost of the Amway product as a percent of the cost of the competing product (i.e., a number over 100 means the Amway product costs more, 200 indicates it costs twice as much, 50 indicates it costs half as much). | | | Also, not having any experience with Amway products myself, I did not feel that I had a basis for comparing Amway manufactured products to store products in terms of effectiveness. |
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http://www.amquix.info/aus/prices.htm
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| | Regularity and Approximation for Hyperbolic Conservation Laws in Several Space Dimensions |
| | ) are regularity spaces for scalar conservation laws in one space dimension, and (ii) there are numerical methods based on moving grids that can achieve arbitrary prescribed orders of approximation, namely, for any initial condition in | | | The primary focus of research sponsored by this grant has been the regularity of solutions to scalar conservation laws and numerical recovery of "shocks" in several space dimensions. | | | Regularity and Approximation for Hyperbolic Conservation Laws in Several Space Dimensions |
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http://www.cs.purdue.edu/ar95/AR95Book-103.html
(6379 words)
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| | MINGLE Homepage |
| | The goal will be to strive for both fast algorithms and high orders of approximation. | | | However, though these kinds of algorithms have already been applied by commercial software companies, the techniques are still in an early phase of development and more (collaborative) effort is needed in order to find optimal algorithms, both from the point of view of approximation error and algorithmic complexity. | | | In order to apply these results to arbitrary meshes however, it is necessary to approximate an arbitrary mesh by a nested one. |
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http://www.cs.technion.ac.il/~vitus/mingle/topic.html
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| | 11th GAMM-Workshop on Multigrid and Hierarchic Solution Techniques : Abstracts : M.A. Schweitzer |
| | The convergence rate $\rho$ of this multilevel solver is independent of the number and the distribution of the discretization points; yet $\rho$ is slightly dependent on the local approximation orders p_i. | | | The shape functions of a partition of unity method are products of piecewise rational partition of unity functions phi_i with supp(phi_i)=\omega_i and higher order local approximation functions \psi_i^n (usually a local polynomial of degree < p_i). | | | A PUM is a generalization of the finite element method (FEM) which does not rely on the availabilty of an appropriate mesh and is hence referred to as a meshfree method. |
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http://www.mis.mpg.de/scicomp/GAMM-WS2003/schweitzer.html
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| | Pade.html |
| | We have conducted some preliminary investigations used SCALAPACK for the inversion and using a range of orders for the Pade' approximation. | | | Let m be the dimension of the smaller null block of K and let n be the dimension of its larger null block. | | | The matrix approximation to EXP(K) employed in SCF minimizations should be accurately orthogonal as well as appropriately close to the exponential value. |
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http://www.emsl.pnl.gov/proj/tms/hpcc_actinides/research-98/argonne/Pade.html
(479 words)
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| | FFTLog |
| | The problem required Fourier transforming a function that extended over many orders of magnitude, and was `smooth' in logarithmic space. | | | From the definition (2) of the continuous Hankel transform, it can be seen that periodically replicating a function a(r) in logarithmic space lnr and then taking its continuous Hankel transform is equivalent to Hankel transforming the function a(r) and then periodically replicating the transform ã(k) in lnk. | | | Usually one is interested in the discrete Fourier or Hankel transform not for its own sake, but rather as an approximation to the continuous transform. |
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http://casa.colorado.edu/~ajsh/FFTLog
(3470 words)
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| | FFTLog |
| | The problem required Fourier transforming a function that extended over many orders of magnitude, and was `smooth' in logarithmic space. | | | Usually one is interested in the discrete Fourier or Hankel transform not for its own sake, but rather as an approximation to the continuous transform. | | | Equations (9) and (10) constitute a discrete Fourier transform pair relating two periodic, linearly spaced sequences a |
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http://casa.colorado.edu/~ajsh/FFTLog
(3470 words)
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