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ON THE CONSTRUCTION OF GAUSSIAN QUADRATURE RULES FROM MODIFIED MOMENTS

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  • المصدر:
    DTIC AND NTIS
  • نوع التسجيلة:
    Electronic Resource
  • الدخول الالكتروني :
    https://apps.dtic.mil/docs/citations/AD0695818
  • معلومة اضافية
    • Publisher Information:
      1969-10
    • Added Details:
      PURDUE UNIV LAFAYETTE IND DEPT OF COMPUTER SCIENCES
      Gautschi,Walter
    • نبذة مختصرة :
      Given a weight function omega(x) on (alpha, beta), and a system of polynomials (p sub k)(x), k = 0 to infinity, with degree p sub k (x) = k, we consider the problem of constructing Gaussian quadrature rules from 'modified moments'. Classical procedures take p sub k (x) = x, but suffer from progressive ill-conditioning as n increases. A more recent procedure, due to Sack and Donovan, takes for p sub k (x) a system of (classical) orthogonal polynomials. The problem is then remarkably well-conditioned, at least for finite intervals (alpha, beta). In support of this observation, we obtain upper bounds for the respective asymptotic condition number. In special cases, these bounds grow like a fixed power of n. We also derive an algorithm for solving the problem considered which generalizes one due to Golub and Welsch. Finally, some numerical examples are presented.
    • الموضوع:
      Theoretical Mathematics; (*NUMERICAL ANALYSIS; THEORY); COMPUTER PROGRAMMING; FOURIER ANALYSIS; POLYNOMIALS; ALGORITHMS; THEOREMS; GAUSSIAN QUADRATURE; ORTHOGONAL FUNCTIONS; Text
    • Note:
      text/html
      English
    • Other Numbers:
      DTICE AD0695818
      831494912
    • Contributing Source:
      From OAIster®, provided by the OCLC Cooperative.
    • الرقم المعرف:
      edsoai.ocn831494912
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