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Math Help - How were these graphs obtained in N.L.S?

  1. #1
    Senior Member bugatti79's Avatar
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    How were these graphs obtained in N.L.S?

    Folks,

    See attached pdf detailing some plots in \mathbb{R}^2. How were these graphs determined for 1-, and \infty- norms?
    Attached Thumbnails Attached Thumbnails How were these graphs obtained in N.L.S?-imag0136.jpg  
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  2. #2
    MHF Contributor
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    Re: How were these graphs obtained in N.L.S?

    For 1-norm, the inequality is |x| + |y| <= 1. You can consider each of the four quadrants and expand |x| and |y| correspondingly. For example, in the second quadrant, x < 0 and y > 0, so |x| = -x and |y| = y. Therefore, the inequality is y - x <= 1, or y <= x + 1.

    For \infty-norm, the inequality is max(|x|, |y|) <= 1, which is equivalent to |x| <= 1 and |y| <= 1, or -1 <= x, y <= 1.
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