Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    3
    ReputationRep:
    Has anyone had ay experience in doing theese types?
    Offline

    11
    ReputationRep:
    (Original post by Mihael_Keehl)
    Has anyone had ay experience in doing theese types?
    Got a particular question?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by joostan)
    Got a particular question?
    I have done this type by doing interpolation took forever lmaoo

    I have dabbled with this type but it seems largerly muddled:

    For this question how do I formulate an equation.
    Spoiler:
    Show
    Say we have: Point of: (-2 -1) (4 59) (3 24) (1 2) (-1 4) (-4 -53)
    Offline

    11
    ReputationRep:
    (Original post by Mihael_Keehl)
    I have done this type by doing interpolation took forever lmaoo

    I have dabbled with this type but it seems largerly muddled:

    For this question how do I formulate an equation.
    Spoiler:
    Show
    Say we have: Point of: (-2 -1) (4 59) (3 24) (1 2) (-1 4) (-4 -53)
    Label your interpolation values, (x_i,f_i) for i=1,. . .,n. Then the polynomial you seek is then a linear combination of the Newton basis polynomials, which are given by: p_{k+1}(x)=\displaystyle\prod_{i  =0}^k(x-x_i) with p_0(x) \equiv 1.
    The coefficients are then given by the Newton divided differences which you can calculate, building up from the given functional values f_i.

    By hand these calculations are, needless to say tedious, though not difficult, the benefit of this method is that the recursive algorithm is useful when writing computer programs to execute the interpolation.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by joostan)
    Label your interpolation values, (x_i,f_i) for i=1,. . .,n. Then the polynomial you seek is then a linear combination of the Newton basis polynomials, which are given by: \displaystyle\prod_{i=1}^n(x-x_i).
    The coefficients are then given by the Newton divided differences which you can calculate, building up from the given functional values f_i.

    By hand these calculations are, needless to say tedious, though not difficult, the benefit of this method is that the recursive algorithm is useful when writing computer programs to execute the interpolation.
    Once you get the values how do you put it into integer form for the polynomial
    Offline

    11
    ReputationRep:
    (Original post by Mihael_Keehl)
    Once you get the values how do you put it into integer form for the polynomial
    What do you mean by integer form?
    Once you compute the values of the coefficients of each approximant p(x)=A_0+\displaystyle\sum_{j=1}  ^n \left( A_j \displaystyle\prod_{i=0}^{j-1}(x-x_i)\right).
    This is itself the polynomial you're looking for. If you so wished, you could expand these out to obtain something of the form: p(x)=\displaystyle\sum_{i=0}^n a_i x^i.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.