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Polynomial-fitting interpolation rules generated by a linear functional

김경중
대한수학회 (The Korean Mathematical Society)|2006.04|대한수학회논문집 (Communications of the KMS)|제21권 제2호|pp. 397-407

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주제분류수학

초록

Abstract

We construct polynomial-fitting interpolation rules to agree witha function f and its first derivative f' at equally spaced nodes on the interval of interest byintroducing a linear functional with which we produce systems oflinear equations. We also introduce a matrix whose determinant isnot zero. Such a property makes it possible to solve the linearsystems and then leads to a conclusion that the rules are uniquelydetermined for the nodes. An example is investigated to comparethe rules with Hermite interpolating polynomials.

참고문헌 (11)

  1. "An Introduction to Numerical Analysis" (1989), John Wiley and Sons
  2. "Operations on Oscillatory Functions" (1997)
  3. "A Gauss Quadrature Rulefor Oscillatory Integrands" (2001)
  4. "Weights of the exponential fitting multistep algorithms forfirst order ODEs" (2001)
  5. "Exponentially fitted variable two-step BDF algorithm forfirst order ODEs" (2003)
  6. "Frequency evaluation in exponential fitting multistep algorithms for ODEs" (2002)
  7. "Two-frequency-dependent Gauss quadraturerules" (2005)
  8. "Quadrature rulesusing first derivatives for oscillatory integrands" (2002)
  9. "Approximate Calculation of Integrals" (1962), Macmillan
  10. "Principles of Mathematical Analysis" (1976), McGRAW-Hill
  11. "Principles of Mathematical Analysis" (1976), McGRAW-Hill

관련 논문AI추천

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