local maxima of a random algebraic polynomial
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ID: 224391
2001
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Abstract
We present a useful formula for the expected number of maxima of a
normal process ξ(t) that occur below a level u. In the
derivation we assume chiefly that ξ(t),ξ′(t), and ξ′′(t) have, with probability one, continuous 1 dimensional
distributions and expected values of zero. The formula referred to
above is then used to find the expected number of maxima below the
level u for the random algebraic polynomial. This result
highlights the very pronounced difference in the behaviour of the
random algebraic polynomial on the interval (−1,1) compared with
the intervals (−∞,−1) and (1,∞). It is also shown
that the number of maxima below the zero level is no longer O(logn) on the intervals (−∞,−1) and (1,∞).
| Reference Key |
farahmand2001internationallocal
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|---|---|
| Authors | ;K. Farahmand;P. Hannigan |
| Journal | structural engineering and mechanics |
| Year | 2001 |
| DOI |
10.1155/S016117120100391X
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| URL | |
| Keywords |
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