F. Chatelin, V. Frayss'e, and T. Braconnier. Computations in the neighbourhood of algebraic singularities. Num. Funct. Anal. Opt., 16:287-- 302, 1995. Home/Search Document Details and Download
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Arnoldi versus Nonsymmetric Lanczos Algorithms for Solving.. - Cullum (1996) (6 citations) (Correct)
....symmetric Lanczos recursion, We would like to be able to answer the question: What spectral properties of A control the convergence of each of these methods We have not answered this question but describe several results which might be useful in such studies. See for example, the related work [2, 3, 4, 5, 6, 7, 8, 27, 28, 29]. In section 2 we outline briefly the Arnoldi and the nonsymmetric Lanczos eigenvalue procedures we are considering. In section 3 we exhibit a certain relationship between these two methods. We prove that given any matrix A and any application of a nonsymmetric Lanczos procedure to A, there exists ....
F. Chatelin, V. Fraysse, and T. Braconnier, Computations in the neighbourhood of algebraic singularities, Numer. Funct. Anal. and Optimiz., 16(3&4) (1995), pp. 287--302.
About the Distance to Singularity for Polynomials in One.. - Chaitin-Chatelin, Gratton (1998) Self-citation (Chatelin) (Correct)
....to inversion. If K(A) is large, and close to 1= Psi, where Psi denotes machine precision, the linear regular system is indistinguishable 2 from a singular system on a computer. In Section 2, we present the different approaches existing in the literature. This problem has been addressed in [3, 11, 5]; see [1] for a good survey. As we shall see, these approaches differ in the way they define the set of singular problems. Throughout this paper, we use the approach of [3] which allow us to understand the behaviour of root finders for polynomials in finite precision (see Example 2.1) In Section ....
....In Section 2, we present the different approaches existing in the literature. This problem has been addressed in [3, 11, 5] see [1] for a good survey. As we shall see, these approaches differ in the way they define the set of singular problems. Throughout this paper, we use the approach of [3] which allow us to understand the behaviour of root finders for polynomials in finite precision (see Example 2.1) In Section 3, we reduce the problem of the distance to singularity to a minimization problem of a function over the complex plane. We investigate in Section 4 the dependence of this ....
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F. Chatelin, V. Frayss'e, and T. Braconnier. Computations in the neighbourhood of algebraic singularities. Num. Funct. Anal. Opt., 16:287-- 302, 1995.
About Hölder Condition Numbers and the.. - Chaitin-Chatelin.. (1999) Self-citation (Chaitin-chatelin) (Correct)
....set to the sets of largest dimension in its stratum. There are 2 different arrows leaving 2 because neither 3 nor is included in the stratum of the other. In our example, A(s) belongs to 3 : it corresponds to the maximal spectral instability possible : the maximal degree of singularity [4]. On the other hand jjA(s) Gamma B(s)jj = jsj, with B(s) Q 0 B 0 1=s 1 0 0 0 0 0 0 1 C AQ defined for any s 6= 0: B(s) belongs to 2 which is in the stratum of 3 . Consequently the limit of the influence of the exact Jordan structure of A(s) is r(A(s) jsj = jjA(s) Gamma ....
F. Chaitin-Chatelin, V. Frayss'e, and T. Braconnier. Computations in the neighbourhood of algebraic singularities. Num. Funct. Anal. Opt., 16, 1995.
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