CS 3220: Introduction to Scientific Computing Steve Marschner - - PowerPoint PPT Presentation

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CS 3220: Introduction to Scientific Computing Steve Marschner - - PowerPoint PPT Presentation

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CS 3220: Introduction to Scientific Computing Steve Marschner Spring 2009 Monday, January 19, 2009 1 scientific computing : The use of computers to solve problems that arise in science (and engineering, medicine, ). numerical methods :

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CS 3220: Introduction to Scientific Computing

Steve Marschner Spring 2009

1 Monday, January 19, 2009

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scientific computing: The use of computers to solve problems that arise in science (and engineering, medicine, …). numerical methods: Algorithms (methods) for solving problems with real numbers by numerical (as opposed to symbolic) means. If your variables represent real-valued quantities, you’re doing numerical computing. Perhaps surprising are:

  • audio (stream of sound pressure samples)
  • video (grids of intensity or color samples)
  • computational geometry (positions in space)
  • computer graphics and vision (geometry, color, light…)
  • information retrieval (more on this in a moment)

with abundant computing power, more applications are using numerical methods all the time.

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Numerical computing in medicine: computed tomography a linear inverse problem

Steven W. Smith—dspguide.com U.S. FDA

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Numerical computing in medicine: computed tomography

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Numerical computing in medicine: computed tomography

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Numerical computing in climatology: predicting global warming partial differential equations

NOAA

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Numerical computing in climatology: predicting global warming

Robert A. Rohde

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Numerical computing in cars: electronic stability control

images from: Liebemann et al. “Safety and Performance Enhancement: The Bosch Electronic Stability Control (ESP)” in The 19th International Technical Conference on the Enhanced Safety of Vehicles (ESV)

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Yaw rate control at work

Fifth Gear—demo of Bosch ESP system

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Numerical computing in cars: electronic stability control

  • rdinary differential equations

Liebemann et al. Liebemann et al.

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Yaw rate control by braking

Fifth Gear—demo of Bosch ESP system

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Numerical computing in autonomous vehicles: path planning

Mark Campbell—Cornell DARPA Urban Challenge team

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Numerical computing in autonomous vehicles: path planning constrained nonlinear optimization

Mark Campbell—Cornell DARPA Urban Challenge team

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Mark Campbell—Cornell DARPA Urban Challenge team

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Mark Campbell—Cornell DARPA Urban Challenge team

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Numerical computing in games: physics engines

  • rdinary differential equations

Crytek GmBH—advertisement for CryEngine 2 game engine

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Numerical computing in movies: realistic lighting

Hand with Reflecting Sphere. M. C. Escher, 1935. lithograph Gene Miller & Ken Perlin, 1982

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Numerical computing in movies: realistic lighting numerical integration (quadrature)

Jonas Unger

Real environment, computed objects

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Numerical computing in movies: camera tracking numerical differentiation nonlinear optimization

Torr & Zisserman, in Vision Algorithms: Theory and Practice, 2000

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Scenespector Systems—VooCAT product demo Zaha Hadid Architects—proposed Guggenheim Vilnius museum

Camera footage Rendered model added

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Numerical computing in information retrieval: Google’s PageRank matrix eigenvalues Idea 1: importance = citation count — simple integer exact answer Idea 2: importance = citation count weighted by importance — now it is a self-referencing definition for a real-valued quantity (and it must be approximated numerically) Computing PageRank works out to be a linear algebra problem: finding the largest eigenvalue of a matrix.

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course themes discrete — continuous exact — approximate accuracy, stability, and robustness “Never in the history of mankind has it been possible to produce so many wrong answers so quickly!” —Carl-Erik Fröberg

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prerequisites calculus, linear algebra some programming experience Matlab CS1132: Transition to Matlab A one-credit course for students who know another language (e.g. Java) and need to map the ideas over to Matlab. Informational meetings: today 3:35 Hollister 307 tomorrow 4:40 Hollister 3:14

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course mechanics http://www.cs.cornell.edu/Courses/cs3220

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