Title: Theory of Birkhoff Interpolation
Publisher: Nova Science Publishers Inc
Book Condition: New
Num Pages: 252 pages. BIC Classification: HP; JFCX; PBC. Category: (G) General (US: Trade); (P) Professional & Vocational. Dimension: 258 x 183 x 22. Weight in Grams: 724. . 2011. Hardcover. . . . . Bookseller Inventory # V9781590336922
Synopsis: Interpolation by polynomials is a very old subject. The first systematic work was due to Newton in the seventeenth century. Lagrange developed his formula only a little later. In 1878 Hermie introduced so called Hermite interpolation. In 1906 Birkhoff published the first paper on lacunary (or Birkhoff) interpolation whose information about a function and its derivatives is irregular. It turns out that the Birkhoff interpolation problem is very difficult. The reasons are: the solvability of the problem is equivalent to non-singularity of the coefficient matrix of higher order, which of course is not easy to determine in general; should the solvability of the problem be known, it is difficult to get an explicit representation of the solution; although an explicit representation of the solution in some special cases can be acquired, it is usually complicated and is hard to study. This book is largely self-contained. It begins with the definitions and elementary properties of Birkhoff interpolation, to be followed by the formulating of the fundamental theorems for regularity and comparison theorems; also investigated are fundamental polynomials of interpolation in details. Various methods and formulas dealing with the theory of Birkhoff's Interpolation follow.
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