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interpolation

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interpolation


  3  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Interpolation  \In*ter`po*la"tion\,  n.  [L.  interpolatio  an 
  alteration  made  here  and  there:  cf  F.  interpolation.] 
  1.  The  act  of  introducing  or  inserting  anything  especially 
  that  which  is  spurious  or  foreign. 
 
  2.  That  which  is  introduced  or  inserted,  especially  something 
  foreign  or  spurious. 
 
  Bentley  wrote  a  letter  .  .  .  .  upon  the  scriptural 
  glosses  in  our  present  copies  of  Hesychius  which  he 
  considered  interpolations  from  a  later  hand.  --De 
  Quincey. 
 
  3.  (Math.)  The  method  or  operation  of  finding  from  a  few 
  given  terms  of  a  series,  as  of  numbers  or  observations, 
  other  intermediate  terms  in  conformity  with  the  law  of  the 
  series. 
 
  From  WordNet  r  1.6  [wn]: 
 
  interpolation 
  n  1:  (mathematics)  calculation  of  the  value  of  a  function  between 
  the  values  already  known 
  2:  an  action  or  remark  that  interrupts  [syn:  {interjection},  {interposition}] 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  interpolation 
 
    A  mathematical  procedure  which 
  estimates  values  of  a  {function}  at  positions  between  listed 
  or  given  values.  Interpolation  works  by  fitting  a  curve" 
  (i.e.  a  function)  to  two  or  more  given  points  and  then 
  applying  this  function  to  the  required  input.  Example  uses 
  are  calculating  {trigonometric  functions}  from  tables  and 
  audio  waveform  sythesis. 
 
  The  simplest  form  of  interpolation  is  where  a  function,  f(x), 
  is  estimated  by  drawing  a  straight  line  ("linear 
  interpolation")  between  the  nearest  given  points  on  either 
  side  of  the  required  input  value: 
 
  f(x)  ~  f(x1)  +  (f(x2)  -  f(x1))(x-x1)/(x2  -  x1) 
 
  There  are  many  variations  using  more  than  two  points  or  higher 
  degree  {polynomial}  functions.  The  technique  can  also  be 
  extended  to  functions  of  more  than  one  input. 
 
  (1997-07-14) 
 
 




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