Skip to main content

Mathematical Foundations of High-Performance Computing and Communications (1991) / Chapter Skim
Currently Skimming:

3 POTENTIAL CONTRIBUTIONS OF THE MATHEMATICAL SCIENCES TO HIGH-PERFORMANCE COMPUTING AND COMMUNICATIONS
Pages 9-14

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 9...
... and robust engineering design for complex industrial processes is being addressed with high-dimensional statistical modeling, which has the potential to contribute greatly. Although these complex processes differ in many specific details, all share the features of having a large number of process stages involving several hundred controllable variables, and a set (often 10 or more)
Read the entire page →
From page 10...
... A rather general theory, developed for stationary spatial stochastic processes and involving Markov random fields, provides a possible tool for modeling the textures that arise in, and confound, this and other inspection applications. Control theory must be introduced into the chip-manufacturing process, in order both to reduce start-up time and to produce quality products.
Read the entire page →
From page 11...
... Currently, each library routine for a distributed memory computer has built-in assumptions about data flow and storage layouts because the underlying mathematical algorithm does not carry information about Hose cno~ces. nor example, tne Data resow or a rest courter transform (FFT)
Read the entire page →
From page 12...
... The improvement of optical fiber technology requires a deeper understanding of many basic problems in nonlinear optics, which can be acquired by a combination of analytical and numerical methods. The effect of noise introduced both by the signal repeaters and by imperfections in the fibers leads to difficult mathematical problems in nonlinear partial differential equations with random coefficients.
Read the entire page →
From page 13...
... Likewise, development of human resources for high-performance computing and communications will continue to rely on contributions from mathematical scientists: computational scientists must be well grounded in the mathematical sciences. More particularly, the education and outreach programs at the nation's established supercomputer centers will continue to reduce the barriers between applied and theoretical scientists and will accelerate the impact of new mathematical models and algorithms on 13
Read the entire page →
From page 14...
... scientists into multidisciplinary groups, which can be an extremely valuable research mode. The very nature of the HPOC program and the grand challenges calls out for such an environment.
Read the entire page →

Key Terms

  • hpcc program
  • partial differential
  • differential equations
  • actual production
  • production process

  • engineering design
  • data storage
  • process diagnostics
  • data flow
  • process flaws

  • computational geometry
  • mathematical researchers
  • help solve
  • major contributions
  • roundoff error

  • mathematical algorithm
  • recast flow
  • technology goals
  • deeper understanding
  • manufacturing faults

  • becoming commonplace
  • carefully designing
  • production data
  • require major
  • develop statistical

  • efficient algorithms
  • efficient sensitivity
  • parallel computers
  • stages involving
  • random fields


    • This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
    More information on Chapter Skim is available.