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POUsing MATLAB to find Minimax Polynomial Approximation of Trigonometric Functions
 

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  1. POUsing MATLAB to find Minimax Polynomial Approximation of Trigonometric Functions
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    <p>I am trying to find the minimax polynomial approximation for sine and cosine using the <strong>remez</strong> exchange algorithm in MATLAB. The need precision out to 23 bits because I am implementing the sine and cosine functions for IEEE-754 floating point.</p> <p>Using this link <a href="http://www.research.scea.com/research/pdfs/RGREENfastermath_GDC02.pdf" rel="nofollow">here</a> (refer to pages 8 through 15), the instructions are given for finding the polynomial using Mathematica and Maple, however, I am not sure how to extrapolate these methods for MATLAB.</p> <p>According to Table 3, I need to use a 5th or 6th order polynomial to get ~23 bits (after the decimal point) of accuracy.</p> <p>I am planning on first performing a range reduction of all incoming theta to between -pi/4 to +pi/4, then performing the sine or cosine function as necessary (The end goal is to implement exp(i*x) = cos(x) + i*sin(x).</p> <p>I might be able to follow the instructions of this paper myself, but I don't know how to use the remez function for my purposes here. Also, I don't follow why the author used equation (6) (on page 9), nor do i understand how the equation for k (on page 11) was determined (where does 2796201 come from?) and why does the defining form of the polynomial we want to end up with change to sin9x) = x + kx^3 + x^5*P(x^2).</p> <p>Would it be better to use the <strong>firpm</strong> function instead (since <strong>remez</strong> is deprecated)?</p> <p>Thank you, all help and guidance are greatly appreciated, as well as edits to ensure the best answer possible to my question.</p>
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    1. CONote that the linked paper already gives a minimax approximation for sin on [0,pi/4] in the section "Optimizing for Floating Point", so you just need to find an approximation for cos on [0,pi/4] and you'll be all set.
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    2. COWell how do you propose I do that?
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    3. COYou got at least one good pointer to a single-precision minimax approximation for cosine on [0,pi/4] in the answers to your previous question: http://stackoverflow.com/questions/9265865/cosine-in-floating-point
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