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Consider the over-determined system Fx = b where $${{\bf F}\in\mathcal{R}^{m \times n}, m \geq n}$$ and rank (F) = r ≤ n, the effective condition number is defined by $${{\rm Cond_{-}eff }= \frac {\|{\bf b}\|}{\sigma_r\|{\bf x}\|}}$$ , where the singular values of F are given as σmax = σ1 ≥ σ2 ≥ . . . ≥ σr > 0 and σr+1 = . . . = σn = 0. For the general perturbed system (A+ΔA...
This paper presents a new algorithm for computing absolutely irreducible components of n-dimensional algebraic varieties defined implicitly by parametric homogeneous polynomial equations over $${\mathbb{Q}}$$ , the field of rational numbers. The algorithm computes a finite partition of the parameters space into constructible sets such that the absolutely irreducible components are given uniformly...
In this paper, a coupled Newton iterative mixed finite element method (MFEM) for solving the stationary conduction–convection problems in two dimension is given. In our method, the Newton iterative MFEM is used for solving all the equations of the conduction–convection problems. The stability and convergence analysis in H1-norm of $${u_h^n, T_h^n}$$ and the L2-norm of $${p_h^n}$$ are derived...
Extending 32-bit DX generators introduced by Deng and Xu (ACM Trans Model Comput Simul 13:299–309, 2003), we perform an extensive computer search for classes of 64-bit and 128-bit DX generators of large orders. The period lengths of these high resolution DX generators are ranging from 101915 to 1058221. The software implementation of these generators can be developed for 64-bit or 128-bit hardware...
In this paper, several two-grid algorithms are presented. For nonsymmetric linear systems, we propose a two-grid algorithm by using the information of the adjoint operator. The solution of the original systems is mainly reduced to a solution of symmetric positive definite (SPD) systems. For nonlinear systems, we present a two-grid algorithm based on the modified Newton method. The solution of the...
For the singular, non-Hermitian, and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the semi-convergence of the Hermitian and skew-Hermitian splitting (HSS) iteration methods. We then investigate the semi-convergence factor and estimate its upper bound for the HSS iteration method. If the semi-convergence condition is satisfied, it...
In some real-world problems solved by machine learning it is compulsory for the solution provided to be comprehensible so that the correct decision can be made. It is in this context that this paper compares bagging (one of the most widely used multiple classifier systems) with the consolidated trees construction (CTC) algorithm, when the learning problem to be solved requires the classification made...
A general procedure to construct ADI methods for multidimensional problems was originated by Beam and Warming using the method of approximate factorization. In this paper, we extend the method of approximate factorization to solve a viscous wave equation. The method can be combined with any implicit linear multistep method for the time integration of the wave equation. The stability of the factored...
This paper investigates the generalized Sylvester-conjugate matrix equation, which includes the normal Sylvester-conjugate, Kalman–Yakubovich-conjugate and generalized Sylvester matrix equations as its special cases. An iterative algorithm is presented for solving such a kind of matrix equations. This iterative method can give an exact solution within finite iteration steps for any initial values...
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