Approximation theory and methods
著者
書誌事項
Approximation theory and methods
Cambridge University Press, 1981
- : pbk
大学図書館所蔵 全56件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
"Related work and references": p. [317]-332
Includes index
内容説明・目次
内容説明
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
目次
- Preface
- 1. The approximation problem and existence of best approximations
- 2. The uniqueness of best approximations
- 3. Approximation operators and some approximating functions
- 4. Polynomial interpolation
- 5. Divided differences
- 6. The uniform convergence of polynomial approximations
- 7. The theory of minimax approximation
- 8. The exchange algorithm
- 9. The convergence of the exchange algorithm
- 10. Rational approximation by the exchange algorithm
- 11. Least squares approximation
- 12. Properties of orthogonal polynomials
- 13. Approximation of periodic functions
- 14. The theory of best L1 approximation
- 15. An example of L1 approximation and the discrete case
- 16. The order of convergence of polynomial approximations
- 17. The uniform boundedness theorem
- 18. Interpolation by piecewise polynomials
- 19. B-splines
- 20. Convergence properties of spline approximations
- 21. Knot positions and the calculation of spline approximations
- 22. The Peano kernel theorem
- 23. Natural and perfect splines
- 24. Optimal interpolation
- Appendices
- Index.
「Nielsen BookData」 より