It is well-known that many Krylov solvers for linear systems, eigenvalue problems, and singular value decomposition problems have very simple and elegant formulas for residual norms. These formulas not only allow us to further understand the methods theoretically but also can be used as cheap stopping criteria without forming approximate solutions and residuals at each step before convergence t...

In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in application meshless method solving PDEs three-dimensional space using multiquadric radial basis functions. It is well known that truncated singular value decomposition (TSVD) most common effective solver ill-conditioned systems, but unfortunately operation count system with ...

Abstract When solving ill-posed inverse problems, a good choice of the prior is critical for computation reasonable solution. A common approach to include Gaussian prior, which defined by mean vector and symmetric positive definite covariance matrix, use iterative projection methods solve corresponding regularized problem. However, main challenge many these that matrix must be known fixed (up c...

In this paper, we are interested in finding an approximate solution $ \hat{\mathcal{X}} of the tensor least-squares minimization problem$ \min_{\mathcal{X}}\left\|\mathcal{X}\times_1A^{(1)}\times_2A^{(2)}\times_3\cdots\times_NA^{(N)}-\mathcal{G}\right\|$, where \mathcal{G}\in \mathbb{R}^{J_1\times J_2\times \cdots \times J_N}$ and A^{(i)}\in \mathbb{R}^{J_i\times I_i} ($ i=1,\ldots,N $) known \...

The concept of the core problem in total least squares (TLS) problems was introduced in [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861–875]. It is based on orthogonal transformations such that the resulting problem decomposes into two independent parts, with one of the parts having trivial (zero) right-hand side and maximal dimensions, and the other part with nonzero...

conclusions small dose of clopidogrel (75 mg) may lead to rare, life-threatening dah, so physicians should be aware of the possibility of dah after neurointervention in patients who have respiratory distress, worsening alveolar infiltrates accompanied by hemoptysis. introduction diffuse alveolar hemorrhage (dah) is a very rare complication but acute and life-threatening event. clopidogrel has g...

interventional techniques aim to find safer and better ways to treat vascular diseases even in many instances, the interventional radiology solutions has been considered the only treatment option for the patients. interventional radiologists are specialists who perform minimally invasive procedures instead of surgery or other treatments. these procedures apply various imaging and catheterizatio...