Numerical Methods in Approximation Theory, Vol. 9 by D. BraessNumerical Methods in Approximation Theory, Vol. 9 by D. Braess

Numerical Methods in Approximation Theory, Vol. 9

byD. BraessEditorL.L. Schumaker

Paperback | October 30, 2012

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This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs­ institut in Oberwolfach during the week of November 24<_302c_20_1991.20_it20_contains20_refereed20_and20_edited20_papers20_by20_2020_of20_the20_4920_participants.20_the20_book20_is20_dedicated20_to20_the20_memory20_of20_prof.20_lothar20_collatz20_who20_mainc2ad_20_tained20_a20_long20_and20_active20_interest20_in20_numerical20_approximation.20_it20_is20_the20_ninth20_in20_a20_series20_of20_volumes20_published20_by20_birkhiiuser20_resulting20_from20_conferences20_on20_the20_subject20_held20_at20_oberwolfach2c_20_and20_co-organized20_by20_prof.20_collatz.20_we20_now20_briefly20_describe20_the20_contents20_of20_the20_book.20_the20_paper20_of20_baszenc2ad_20_ski2c_20_delvos20_and20_jester20_deals20_with20_blending20_using20_sine20_double20_series20_expanc2ad_20_sions20_of20_functions20_defined20_on20_the20_unit20_square.20_in20_addition20_to20_giving20_explicit20_error20_estimates20_for20_partial20_sums20_and20_for20_interpolating20_sine20_polynomials2c_20_they20_also20_show20_that20_boolean20_sums20_yield20_almost20_the20_same20_asymptotic20_error20_estimates20_as20_the20_conventional20_tensor-product20_approach2c_20_but20_with20_a20_reduced20_number20_of20_terms.20_the20_paper20_of20_beatson20_and20_light20_discusses20_approximation20_by20_quasic2ad_20_interpolants20_which20_are20_sums20_of20_scaled20_translates20_of20_a20_one-parameter20_family20_of20_functions.20_they20_do20_not20_require20_reproduction20_of20_low20_degree20_polynomials2c_20_but20_nevertheless20_are20_able20_to20_give20_error20_bounds20_and20_analyze20_quasi-interpolation20_based20_on20_gaussians20_and20_exponentials.20_binev20_and20_jetter20_deal20_with20_multivariate20_interpolation20_using20_shifts20_of20_a20_single20_basis20_function.20_they20_treat20_both20_gridded20_data20_and20_scattered20_data.20_as20_examples2c_20_they20_consider20_box20_splines20_and20_certain20_radial20_basis20_functions. 1991.="" it="" contains="" refereed="" and="" edited="" papers="" by="" 20="" of="" the="" 49="" participants.="" book="" is="" dedicated="" to="" memory="" prof.="" lothar="" collatz="" who="" _mainc2ad_="" tained="" a="" long="" active="" interest="" in="" numerical="" approximation.="" ninth="" series="" volumes="" published="" birkhiiuser="" resulting="" from="" conferences="" on="" subject="" held="" at="" _oberwolfach2c_="" co-organized="" collatz.="" we="" now="" briefly="" describe="" contents="" book.="" paper="" _baszenc2ad_="" _ski2c_="" delvos="" jester="" deals="" with="" blending="" using="" sine="" double="" _expanc2ad_="" sions="" functions="" defined="" unit="" square.="" addition="" giving="" explicit="" error="" estimates="" for="" partial="" sums="" interpolating="" _polynomials2c_="" they="" also="" show="" that="" boolean="" yield="" almost="" same="" asymptotic="" as="" conventional="" tensor-product="" _approach2c_="" but="" reduced="" number="" terms.="" beatson="" light="" discusses="" approximation="" _quasic2ad_="" interpolants="" which="" are="" scaled="" translates="" one-parameter="" family="" functions.="" do="" not="" require="" reproduction="" low="" degree="" nevertheless="" able="" give="" bounds="" analyze="" quasi-interpolation="" based="" gaussians="" exponentials.="" binev="" jetter="" deal="" multivariate="" interpolation="" shifts="" single="" basis="" function.="" treat="" both="" gridded="" data="" scattered="" data.="" _examples2c_="" consider="" box="" splines="" certain="" radial="">
Title:Numerical Methods in Approximation Theory, Vol. 9Format:PaperbackDimensions:359 pages, 23.5 × 15.5 × 1.73 inPublished:October 30, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034897022

ISBN - 13:9783034897020

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Table of Contents

Blending Approximations with Sine Functions.- Quasi-interpolation in the Absence of Polynomial Reproduction.- Estimating the Condition Number for Multivariate Interpolation Problems.- Wavelets on a Bounded Interval.- Quasi-Kernel Polynomials and Convergence Results for Quasi-Minimal Residual Iterations.- Rate of Approximation of Weighted Derivatives by Linear Combinations of SMD Operators.- Approximation by Multivariate Splines: an Application of Boolean Methods.- Lm,?,s-Splines in ?d.- Constructive Multivariate Approximation via Sigmoidal Functions with Applications to Neural Networks.- Spline-Wavelets of Minimal Support.- Necessary Conditions for Local Best Chebyshev Approximations by Splines with Free Knots.- C1 Interpolation on Higher-Dimensional Analogs of the 4-Direction Mesh.- Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid.- The L2-Approximation Orders of Principal Shift-Invariant Spaces Generated by a Radial Basis Function.- A Multi-Parameter Method for Nonlinear Least-Squares Approximation.- Analog VLSI Networks.- Converse Theorems for Approximation on Discrete Sets II.- A Dual Method for Smoothing Histograms using Nonnegative C1-Splines.- Segment Approximation By Using Linear Functionals.- Construction of Monotone Extensions to Boundary Functions.