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Math Help - Cubic interpolation

  1. #1
    Newbie
    Joined
    Jul 2011
    Posts
    1

    Cubic interpolation

    Helle there,

    I am currently studying fixed-income market securities as part of a master's degree in Finance, but I seem to have a problem that involves understanding something that seems basic, but since I lack knowledge of any form of Matrix' solving, I suppose the question will do just fine in the Pre-University Math Help forums.

    I need to find the interpolated rate R(0,w) with w [v;z] verifieying the three-order polynomial equation: R(0,w) = aw^3 + bw^2 + cw + d

    where a, b, c and d sitisfy the system:

    R(0,v) = av^3 + bv^2 + cv + d
    R(0,x) = ax^3 + bx^2 + cx + d
    R(0,y) = ay^3 + by^2 + cy + d
    R(0,z) = az^3 + bz^2 + cz + d

    I need to solve this cubic polynomial function by solving a matrix:

    a
    b
    c
    d

    equals

    1 1 1 1
    8 4 2 1
    27 9 3 1
    64 16 4 1

    by

    3%
    5%
    5,5%
    6%


    Then what I don't understand, is that it (my book) shows me solve for the vector of constants a, b, c and d by:

    x = B^(-1)*A, where x are the constant, B the matrix of maturity terms and A the vector of interest rate (3%, 5%, etc.).

    The answers are:
    0.0025
    -0.0225
    0.07
    -0.02

    I might not even need to know this, but I am currently deeply frustrated by not being able to understand this

    Who can help me out here?

    Regards,

    Hans
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  2. #2
    MHF Contributor

    Joined
    Apr 2005
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    1121

    Re: Cubic interpolation

    Since you have the formula x= B^{-1}A which uses the "inverse" of B, do you know how to find the inverse of a matrix? Or do you know how to do "row reduction" of a matrix?

    You might find these interesting:
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