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1: Bibliography X
  • H. Xiao, V. Rokhlin, and N. Yarvin (2001) Prolate spheroidal wavefunctions, quadrature and interpolation. Inverse Problems 17 (4), pp. 805–838.
  • 2: 3.3 Interpolation
    §3.3 Interpolation
    §3.3(i) Lagrange Interpolation
    Linear Interpolation
    §3.3(v) Inverse Interpolation
    §3.3(vi) Other Interpolation Methods
    3: Annie A. M. Cuyt
    A lot of her research has been devoted to rational approximations, in one as well as in many variables, and sparse interpolation. …
    4: 3.4 Differentiation
    The B k n are the differentiated Lagrangian interpolation coefficients:
    3.4.2 B k n = d A k n / d t ,
    3.4.7 h f t = k = 1 2 B k 3 f k + h R 3 , t , 1 < t < 2 ,
    3.4.11 h f t = k = 2 3 B k 5 f k + h R 5 , t , 2 < t < 3 ,
    3.4.15 h f t = k = 3 4 B k 7 f k + h R 7 , t , 3 < t < 4 ,
    5: Philip J. Davis
    Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky. …
    6: 3.8 Nonlinear Equations
    Regula Falsi
    Inverse linear interpolation3.3(v)) is used to obtain the first approximation: …
    7: Bibliography N
  • National Bureau of Standards (1944) Tables of Lagrangian Interpolation Coefficients. Columbia University Press, New York.
  • 8: Bibliography P
  • M. J. D. Powell (1967) On the maximum errors of polynomial approximations defined by interpolation and by least squares criteria. Comput. J. 9 (4), pp. 404–407.
  • 9: Bibliography T
  • L. N. Trefethen (2011) Six myths of polynomial interpolation and quadrature. Math. Today (Southend-on-Sea) 47 (4), pp. 184–188.
  • 10: 3.11 Approximation Techniques
    If J = n + 1 , then p n ( x ) is the Lagrange interpolation polynomial for the set x 1 , x 2 , , x J 3.3(i)). … For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating f ( x ) on the complete interval [ a , b ] . …