منابع مشابه
Recurrence Relations and Asymptotics for Four - Manifold
The polynomial invariants qd for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the polynomials. As an application, one can read off a lower bound for the genera of embedded surfaces from the asymptotics of qd for large d. The relations are proved u...
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We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.
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Several three-term recurrence relations for confluent hypergeometric functions are analyzed from a numerical point of view. Minimal and dominant solutions for complex values of the variable z are given, derived from asymptotic estimates of Whittaker functions with large parameters. The Laguerre polynomials and the regular Coulomb wave functions are studied as particular cases, with numerical ex...
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The performance attributes of a broad class of randomised algorithms can be described by a recurrence relation of the form T(x) = a(x)+T(H(x)), where a is a function and H(x) is a random variable. For instance, T(x) may describe the running time of such an algorithm on a problem of size x. Then T(x) is a random variable, whose distribution depends on the distribution of H(x). To give high proba...
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This paper presents explicit formulas and algorithms to compute the eigenvalues and eigenvectors of order-one-quasiseparable matrices. Various recursive relations for characteristic polynomials of their principal submatrices are derived. The cost of evaluating the characteristic polynomial of an N × N matrix and its derivative is only O(N). This leads immediately to several versions of a fast q...
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2010
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081080903125415