Optimal rational starting approximations
نویسندگان
چکیده
منابع مشابه
Optimal Starting Approximations for Newton's Method
Abstract. Various writers have dealt with the subject of optimal starting approximations for square-root calculation by Newton's method. Three optimality criteria that have been used can be shown to lead to closely related approximations. This fact makes it surprisingly easy to choose a starting approximation of some prescribed form so that the maximum relative error after any number of Newton ...
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Abstra t. We solve vis ous Burger's equation using a fast and a urate algorithm referred to here as the redu tion algorithm for omputing near optimal rational approximations. Given a proper rational fun tion with n poles, the redu tion algorithm omputes (for a desired L ∞ -approximation error) a rational approximation of the same form, but with a (near) optimally small number m ≪ n of poles. Al...
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Abstra t. The need to ompute small on-eigenvalues and the asso iated on-eigenve tors of positive-de nite Cau hy matri es naturally arises when onstru ting rational approximations with a (near) optimally small L error. Spe i ally, given a rational fun tion with n poles in the unit disk, a rational approximation with m ≪ n poles in the unit disk may be obtained from the mth on-eigenve tor of an n...
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The continuous-time persistent disturbance rejection prohlem (L1 optimal control) leads to nonrational compensators, even for SISO systems [4], [7], [SI. As noted in [4], the difficulty of physically implementing these controllers suggest that the most significant applications of the continuous time L1 theory is to furnish bounds for the achievable performance of the plant. Recently, two differ...
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Abstra t. We introdu e a new omputationally e ient algorithm for onstru ting near optimal rational approximations of large (onedimensional) data sets. In ontrast to wavelet-type approximations, these new approximations are e e tively shift invariant. We note that the omplexity of urrent algorithms for omputing near optimal rational approximations prevents their use for large data sets. In order...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1974
ISSN: 0021-9045
DOI: 10.1016/0021-9045(74)90047-1