Everand Logo

Welcome to Everand!

  • Discover millions of ebooks, audiobooks, and so much more with a free trial

    Only $11.99/month after trial. Cancel anytime.

    Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates
    Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates
    Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates
    Ebook492 pages3 hours

    Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates

    By Pekka Neittaanmäki and Sergey R. Repin

    ()

    Read preview

    About this ebook

    Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.

    In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.

    The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.

    · computable bounds of approximation errors
    · checking algorithms
    · iteration processes
    · finite element methods
    · elliptic type problems
    · nonlinear variational problems
    · variational inequalities
    LanguageEnglish
    PublisherElsevier Science
    Release dateSep 4, 2004
    ISBN9780080540504
    Reliable Methods for Computer Simulation: Error Control and Posteriori Estimates
    Author

    Pekka Neittaanmäki

    Pekka Neittaanmäki is Professor at University of Jyväskylä and the UNESCO Chair on Digital Platforms for Emerging Economies. He is the author of 50 books and 300 articles. He is on the Board of 10 journals and academic associations and has received 10 honorable awards. His research is on digital platform economics and information technology industrial applications.

    Read more from Pekka Neittaanmäki

    Related authors

    Related to Reliable Methods for Computer Simulation

    Titles in the series (23)

    View More
    View More

    Related ebooks

    Mathematics For You

    View More
    View More

    Related podcast episodes

    Related articles

    • Article

      How Spooky Science Helps Us Peer Inside The Planets

      Dec 3, 2020

      An assistant professor of computational science at the EPFL research centre in Lausanne, Switzerland, involved in the current research on metallic hydrogen. Could you explain how the machine-learning techniques used in your research work? Why were th

      1 min read

    • Article

      Business applications For Quantum computing

      May 1, 2022

      COMPUTERS DO ARITHMETIC. Underlying every amazing application of computers today is math, calculated using binary digits or ‘bits.’ The original computers of the early 1950s could perform about 465 multiplications per second — much faster than the ‘h

      11 min read

    • Article

      Chinese Students' Dream Device Defeats Japan's Most Powerful Supercomputer In World Contest

      Jun 15, 2022

      A small computer developed by Chinese students outperformed Japan's most powerful machine in solving a major complex data problem related to artificial intelligence, according to the latest global ranking. Supercomputer Fugaku in Japan has nearly 4 m

      3 min read

    • Article

      Are Neural Networks About to Reinvent Physics?

      Nov 21, 2019

      Can AI teach itself the laws of physics? Will classical computers soon be replaced by deep neural networks? Sure looks like it, if you’ve been following the news, which lately has been filled with headlines like, “A neural net solves the three-body p

      9 min read

    • Article

      Moore’s Law Is About to Get Weird: Never mind tablet computers. Wait till you see bubbles and slime mold.

      Feb 12, 2015

      I’ve never seen the computer you’re reading this story on, but I can tell you a lot about it. It runs on electricity. It uses binary logic to carry out programmed instructions. It shuttles information using materials known as semiconductors. Its brai

      7 min read

    • Article

      Folding@home In Practice

      Jul 20, 2021

      A computational chemist undertaking a postdoctoral study at the KTH Royal Institute of Technology in Stockholm, Sweden, Sergio Perez Conesa uses Folding@home in the hope of uncovering a new drug or treatment for common illnesses associated with ion c

      5 min read

    • Article

      Is Artificial Intelligence Permanently Inscrutable?: Despite new biology-like tools, some insist interpretation is impossible.

      Sep 1, 2016

      Dmitry Malioutov can’t say much about what he built. As a research scientist at IBM, Malioutov spends part of his time building machine learning systems that solve difficult problems faced by IBM’s corporate clients. One such program was meant for a

      13 min read

    • Article

      The Mathematics Of Contagion

      Apr 21, 2020

      The Mathematics Of Contagion
      4 min read

    • Article

      Readers’comments

      Oct 8, 2020

      Readers’comments
      4 min read

    • Article

      Is Artificial Intelligence Permanently Inscrutable?

      Sep 1, 2016

      Dmitry Malioutov can’t say much about what he built. As a research scientist at IBM, Malioutov spends part of his time building machine learning systems that solve difficult problems faced by IBM’s corporate clients. One such program was meant for a

      13 min read

    • Article

      DeepMind AI Predicts Acute Loss Of Kidney Function Two Days In Advance, Study Shows

      Jul 31, 2019

      DeepMind's AI was able to predict 90% of acute kidney injury episodes that required dialysis, with a lead time of 48 hours.

      2 min read

    • Article

      Even The Best Artificial Intelligence Has Weaknesses

      Jan 16, 2024

      New research tries to reveal the weaknesses in artificial intelligence. Machines interpret medical scanning images more accurately than doctors, they translate foreign languages, and may soon be able to drive cars more safely than humans. However, ev

      2 min read

    • Article

      Bundles Of Energy

      Jun 4, 2023

      Bundles Of Energy
      9 min read

    Related categories

    Reviews for Reliable Methods for Computer Simulation

    0 ratings

    0 ratings0 reviews

    What did you think?

    Tap to rate

    Review must be at least 10 words

      Book preview

      Reliable Methods for Computer Simulation - Pekka Neittaanmäki

      1^book_preview_excerpt.html[nG~hDR%&-KICQ5YUiVU*l]f/s[ O`uO_DdOwS0|]?_|}P>1Թ.3?U7ÃojWfS7۪jئѺ,~*,znVT]_~ɟxsm3Ә'm=iS[UxؤlTfR(oL:3Jպm6̙-LmSuW&STmj2a5vЍgPFzlWЍ*Rgz!Fi*I%maz t~ ×sL-6]ЋwS&: -al1V2u>4ݓWE]6KGyp?wP&\l MkJȋ23;@-};LšxVmY[y_ .3]2 ݆j+.=BW|ZFJ :h3 KXxsq 8jNAaRW/p4 NF;7nv ej-p2lFl2c0@cbNp| (:{@y]|צWh/.[ b-t`}zh`w%bNf.%!YN# nϺ@_\ʉ3{O+gEw6 bfmiD=1PW$4|r+}6k2R4n$WWaY[2nͪ2@_ #qjxJ}Ej]6<[6ds%/C` ]#I\.}sSкvn!dO4u0/DNVC;dlUX㺤Cmq/ Ƀު8 / %pGt^ӑאPQƓڒQ\@h*m r* !$zt񮇹$(` Y[~+%d)3V:(OF? 1NI;c[@_搝F tI~_|sm[VnKK Aƽb VU0.~H=ĊtX{xZ=FqO[4b&`zMajfni5@7"`VbZ罥e2D${YLE D" !icr2pѪh<11NT,X8pplTy?s>\*$$w>oOL(Y%tX{z,JzcĠH~x,ٸr^2rx0{gvF!ED! N(.p:p2( VL~nBg.h Ù;*FxLKJ1~hPNws֩& dҾXy[] Q=<9t>tL7uQCNÔ[I/\nl&/'f`TEToXpL*ve!jWn) '} d`>"Ba,d.HHk9q&(; çH0.(\υ,6Xw("2 J-JK@[+db@[|_9EEȗNN XN\FpF 6vY Uؑ5@'CJ1 ca}CcNl% ue|'05g8\:OM&7Co޽ D)+ÿ>|yߦWkYLު?W c_@! ,Tu_]hvp69ĝ]{?`kKZ`h캗d͑:rawslsƿv W@MZ]ѧXИ7aiĪQ;Q/ݶ :DI-u}΢).2TbI?h k@^I?x\{Ket'Wm )е5^.QBW<d;SQѧrU*a6ܛXSeTDQyg͒>XU-lI(הOdY 8X"*Aw4ƃ [~\n}bsN ë\*T,D٩%\ڮ->_ls$}:V]Qͻ=\?Ԝ=)6 /C56ܹO_?ۆ c6@Z,B<04IPk4grFh3mnag0ŌBM%+  DI|]qi>^=~OEo[g@`?N㛽14hh"kI٨N07Ѓ]˿[0$k0O@s4*R#9Gw^>تOO>Z[j3noǛ+5}GOmxD:}9zr%Sga F_0o>﬽*p }!du%^/k+okROlP?4$Qrk1m/˞%L$$.!gJ}FGmIHh0tdTk'PR n-<\t [ nfԱFn=*j:E? <l25m)H8Ȭ>6s _$yw7<+iYLKllml;0ߨd @"l&ݺ΀[q=rn> džA6@Bymy rt߽=rݝ+7/OyV 3->}>W&[ό|< cU( eN`#mq.v?)0ObA{7Jsq&ƏʫG ۦɇmޱrlӿ+ 4!jp)GrnH!s]e$`G0̥k0غ|WnDs…t yFp(IP5XL6aל<͊,/ݏNP"L\Jg 0;4@%Lkh3 ^FaF3^AͥođcC+eJ["9݄ L=^փ]9mݥ=} QPV2S/*]/h)\
      Enjoying the preview?
      Page 1 of 1