共查询到20条相似文献,搜索用时 15 毫秒
1.
We give an elementary calculus proof of the asymptotic formulas for the zeros of the q-sine and cosine functions which have been recently found numerically by Gosper and Suslov. Monotone convergent sequences of the lower and upper bounds for these zeros are constructed as an extension of our method. Improved asymptotics are found by a different method using the Lagrange inversion formula. Asymptotic formulas for the points of inflection of the basic sine and cosine functions are conjectured. Analytic continuation of the q-zeta function is discussed as an application. An interpretation of the zeros is given. 相似文献
2.
《Journal of Complexity》2000,16(1):265-273
The recently proposed Chebyshev-like lifting map for the zeros of a univariate polynomial was motivated by its applications to splitting a univariate polynomial p(z) numerically into factors, which is a major step of some most efficient algorithms for approximating polynomial zeros. We complement the Chebyshev-like lifting process by a descending process, decrease the estimated computational cost of performing the algorithm, demonstrate its correlation to Graeffe's lifting/descending process, and generalize lifting from Graeffe's and Chebyshev-like maps to any fixed rational map of the zeros of the input polynomial. 相似文献
3.
This paper is a continuation of our recent work on the localization of the eigenvalues of matrices. We give new bounds for the real and imaginary parts of the eigenvalues of matrices. Applications to the localization of the zeros of polynomials are also given. 相似文献
4.
Ravi P. Agarwal Donal O'Regan 《Proceedings of the American Mathematical Society》2001,129(4):1015-1020
A new fixed point theorem for Mönch maps on locally convex spaces is given. In addition, a continuation theorem for Mönch maps is presented.
5.
M. Giusti G. Lecerf B. Salvy J.-C. Yakoubsohn 《Foundations of Computational Mathematics》2007,7(1):1-58
Isolated multiple zeros or clusters of zeros of analytic maps with several variables are known to be difficult to locate and
approximate. This paper is in the vein of the α-theory, initiated by M. Shub and S. Smale in the beginning of the 1980s.
This theory restricts to simple zeros, i.e., where the map has corank zero. In this paper we deal with situations where the
analytic map has corank one at the multiple isolated zero, which has embedding dimension one in the frame of deformation theory.
These situations are the least degenerate ones and therefore most likely to be of practical significance. More generally,
we define clusters of embedding dimension one. We provide a criterion for locating such clusters of zeros and a fast algorithm
for approximating them, with quadratic convergence. In the case of a cluster with positive diameter
our algorithm stops at a distance of the cluster which is about its diameter. 相似文献
6.
Summary Using the argument principle higher order methods for simultaneous computation of all zeros of generalized polynomials (like algebraic, trigonometric and exponential polynomials or exponential sums) are derived. The methods can also be derived following the continuation principle from [3]. Thereby, the unified approach of [7] is enlarged to arbitrary orderN. The local convergence as well as a-priori and a-posteriori error estimates for these methods are treated on a general level. Numerical examples are included. 相似文献
7.
A.J Tromba 《Journal of Functional Analysis》1976,23(4):362-368
We define the notion of a Fredholm vector field and prove a transversality result giving conditions under which a vertical family of such vector fields generically have nondegenerate zeros. Many geometric objects like minimal surfaces, geodesics, and harmonic maps arise as the zeros of a Fredholm vector field. 相似文献
8.
We describe maps preserving zeros of multilinear Lie polynomials of degrees 3 and 4 on prime algebras and matrices over unital algebras. In particular, our theorems generalize several results related to commutativity preserving maps. 相似文献
9.
David Ariza-Ruiz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(5):1628-1640
In [5], Zamfirescu (1972) gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan, and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given. 相似文献
10.
J. M. Soriano 《Czechoslovak Mathematical Journal》2011,61(1):65-72
Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined
between any two Banach spaces over $
\mathbb{K}
$
\mathbb{K}
has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout
the entire space. The proof of the result is constructive and is based upon a continuation method. 相似文献
11.
D. O'Regan 《Mathematical and Computer Modelling》1999,30(11-12)
Several continuation principles are presented for “essential” type maps. Our analysis relies only on Urysohn's Lemma. 相似文献
12.
Generalized eigenvalue problems can be considered as a system of polynomials. The homotopy continuation method is used to find all the isolated zeros of the polynomial system which corresponds to the eigenpairs of the generalized eigenvalue problem. A special homotopy is constructed in such a way that there are exactly n distinct smooth curves connecting trivial solutions to desired eigenpairs. Since the curves followed by general homotopy curve following scheme are computed independently of one another, the algorithm is a likely candidate for exploiting the advantages of parallel processing to the generalized eigenvalue problems. 相似文献
13.
The maximal number of zeros of multi-dimensional real analytic maps with small parameter is studied by means of the multi-dimensional generalization of Rouché's theorem. The obtained result is applied to study the maximal number of periodic solutions to multi-dimensional differential systems. An application to a class of three-dimensional autonomous systems is given. 相似文献
14.
We consider the procedure for analytic continuation of the replica matrix. We formulate a particular form of this procedure
in which the analytic continuation is defined by a sequence of maps. Using this definition, we construct a solution that breaks
the Parisi replica symmetry and find the corresponding p-adic pseudodifferential operator.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 336–341, August, 2005 相似文献
15.
Donal O'Regan 《Applicable analysis》2013,92(9):1944-1958
In this article, we present a definition of d-essential and d–L-essential maps in completely regular topological spaces and we establish a homotopy property for both d-essential and d–L-essential maps. Also using the notion of extendability, we present new continuation theorems. 相似文献
16.
Donal O’Regan 《Applicable analysis》2013,92(8):1674-1690
In this paper, we present new continuation theorems for maps in a very general class. 相似文献
17.
The Dirichlet problem for harmonic maps from Riemannian polyhedra to spaces of upper bounded curvature 总被引:1,自引:0,他引:1
Bent Fuglede 《Transactions of the American Mathematical Society》2005,357(2):757-792
This is a continuation of the Cambridge Tract ``Harmonic maps between Riemannian polyhedra', by J. Eells and the present author. The variational solution to the Dirichlet problem for harmonic maps with countinuous boundary data is shown to be continuous up to the boundary, and thereby uniquely determined. The domain space is a compact admissible Riemannian polyhedron with boundary, while the target can be, for example, a simply connected complete geodesic space of nonpositive Alexandrov curvature; alternatively, the target may have upper bounded curvature provided that the maps have a suitably small range. Essentially in the former setting it is further shown that a harmonic map pulls convex functions in the target back to subharmonic functions in the domain.
18.
M. Giusti G. Lecerf B. Salvy J.-C. Yakoubsohn 《Foundations of Computational Mathematics》2005,5(3):257-311
At the beginning of the 1980s, M. Shub and S. Smale developed a
quantitative analysis of Newton's method for multivariate analytic
maps. In particular, their α-theory gives an effective
criterion that ensures safe convergence to a simple isolated zero.
This criterion requires only information concerning the map at the
initial point of the iteration. Generalizing this theory to multiple
zeros and clusters of zeros is still a challenging problem. In this
paper we focus on one complex variable function. We study general
criteria for detecting clusters and analyze the convergence of
Schroder's iteration to a cluster. In the case of a multiple root,
it is well known that this convergence is quadratic. In the case of a
cluster with positive diameter, the convergence is still quadratic
provided the iteration is stopped sufficiently early. We propose a
criterion for stopping this iteration at a distance from the cluster
which is of the order of its diameter. 相似文献
19.
Donal O'Regan 《Applicable analysis》2013,92(5):503-513
A number of new continuation theorems are presented for maps defined on closed subsets of a Fréchet space E. The proofs rely on the notion of an essential map and on viewing E as the projective limit of a sequence of Banach spaces. 相似文献
20.
Ling Yang 《Calculus of Variations and Partial Differential Equations》2009,35(4):409-420
For an arbitrary Dirac-harmonic map (φ,ψ) between compact oriented Riemannian surfaces, we shall study the zeros of |ψ|. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of |ψ| and the genus of M and N. On the basis, we could clarify all of non-trivial Dirac-harmonic maps from S
2 to S
2. 相似文献