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...

The partial least squares (PLS) method computes a sequence of approximate solutions xk ∈ Kk(AA,A b), k = 1, 2, . . . , to the least squares problem minx ‖Ax− b‖2. If carried out to completion, the method always terminates with the pseudoinverse solution x† = A†b. Two direct PLS algorithms are analyzed. The first uses the Golub–Kahan Householder algorithm for reducing A to upper bidiagonal form....

We describe the development of a method for the efficient computation of the smallest singular values and corresponding vectors for large sparse matrices [4]. The method combines state-of-the-art techniques that make it a useful computational tool appropriate for large scale computations. The method relies upon Lanczos bidiagonalization (LBD) with partial reorthogonalization [6], enhanced with ...

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...