Numerical Analysis and Its Applications: Second by Haiscam Abdallah, Moulaye Hamza (auth.), Lubin Vulkov,

By Haiscam Abdallah, Moulaye Hamza (auth.), Lubin Vulkov, Plamen Yalamov, Jerzy Waśniewski (eds.)

This e-book constitutes the completely refereed post-proceedings of the second one overseas convention on Numerical research and Its functions, NAA 2000, held in Rousse, Bulgaria in June 2000.
The ninety revised papers provided have been rigorously chosen for inclusion within the publication in the course of the rounds of inspection and reviewing. All present features of numerical research are addressed. one of the program fields coated are computational sciences and engineering, chemistry, physics, economics, simulation, and so forth.

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Extra resources for Numerical Analysis and Its Applications: Second InternationalConference, NAA 2000 Rousse, Bulgaria, June 11–15, 2000 Revised Papers

Example text

Let us note Table 1. 1 0 10 20 time (days) 30 error -4 1 0 x 10 0 10 20 30 time (days) Fig. 1. ) and the eccentricity e for 30 days. ) and in the eccentricity e for 30 days in a seminumerical integration of the Low orbit that for a complete analytical theory of an artificial satellite is usual to have thousands or, even, millions of terms [1]. In Figure 1 we show the evolution, in the osculating and averaged elements, of the semimajor axis and the eccentricity of the Low orbit calculated with the seminumerical scheme.

We consider the following inner product and norm. Definition 1 (inner product, norm). Consider the subspace P ⊂ C[z]3×1 of polynomial vectors P of degree   n deg P =  s  . 0 Given the points zk ∈ C and the weight vectors Fk = λ1,k λ2,k λ3,k ∈ C1×3 , k = 1, 2, . . , M, we define the discrete inner product P, Q for two polynomial vectors P, Q ∈ P as follows: M P, Q := k=1 P H (zk )FkH Fk Q(zk ). (5) An Algorithm for Toeplitz Least Squares Problems 31 The norm P of a polynomial vector P ∈ P is defined as: P := P, P .

Numerical experiments show that this approach is not only efficient but also numerically stable, even if the coefficient matrix is very ill-conditioned. In this paper we will also develop a numerically stable method that works for ill-conditioned problems—in other words, for problems that cannot be solved via the normal equations approach. We proceed as follows. The original LSproblem is first embedded into a larger LS-problem. The coefficient matrix of the latter problem has additional structure: it is a circulant block matrix.

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