• 대한수학회지
• /
• 제52권2호
• /
• pp.349-372
• /
• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• ETRI Journal
• /
• 제28권2호
• /
• pp.155-161
• /
• 2006

In this paper, we introduce an escalator (ESC) algorithm based on the least squares (LS) criterion. The proposed algorithm is relatively insensitive to the eigenvalue spread ratio (ESR) of an input signal and has a faster convergence speed than the conventional ESC algorithms. This algorithm exploits the fast adaptation ability of least squares methods and the orthogonalization property of the ESC structure. From the simulation results, the proposed algorithm shows superior convergence performance.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.409-417
• /
• 2003

There are two rotation matrix parameters in a model, pro-posed by Prentice in 1989, for pairs of rotations in 3 dimensional space. For the least squares estimates of the two parameters, an algorithm was also presented, but it turned out that the algorithm could fail to get the least squares estimates. This article provides another algorithm for the least squares estimates and its performance is demonstrated by simulation results.

• Journal of applied mathematics & informatics
• /
• 제6권3호
• /
• pp.757-770
• /
• 1999

We analyse in this paper the possibility of using preconditioning techniques as for square non-singular systems, also in the case of inconsistent least-squares problems. We find conditions in which the minimal norm solution of the preconditioned least-wquares problem equals that of the original prblem. We also find conditions such that thd Kaczmarz-Extendid algorithm with relaxation parameters (analysed by the author in [4]), cna be adapted to the preconditioned least-squares problem. In the last section of the paper we present numerical experiments, with two variants of preconditioning, applied to an inconsistent linear least-squares model probelm.

• The Journal of the Acoustical Society of Korea
• /
• 제22권3E호
• /
• pp.93-100
• /
• 2003

We present a recursive total least squares (RTLS) algorithm for adaptive system identification. So far, recursive least squares (RLS) has been successfully applied in solving adaptive system identification problem. But, when input data contain additive noise, the results from RLS could be biased. Such biased results can be avoided by using the recursive total least squares (RTLS) algorithm. The RTLS algorithm described in this paper gives better performance than RLS algorithm over a wide range of SNRs and involves approximately the same computational complexity of O(N²).

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1233-1245
• /
• 2008

In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.

• 대한수학회지
• /
• 제54권5호
• /
• pp.1557-1571
• /
• 2017

The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제11권5호
• /
• pp.2523-2538
• /
• 2017

In most of the existing literature, the definition of the class label has the following characteristics. First, the class label of the samples from the same object has an absolutely fixed value. Second, the difference between class labels of the samples from different objects should be maximized. However, the appearance of a face varies greatly due to the variations of the illumination, pose, and expression. Therefore, the previous definition of class label is not quite reasonable. Inspired by discriminative least squares regression algorithm (DLSR), a noisy label based discriminative least squares regression algorithm (NLDLSR) is presented in this paper. In our algorithm, the maximization difference between the class labels of the samples from different objects should be satisfied. Meanwhile, the class label of the different samples from the same object is allowed to have small difference, which is consistent with the fact that the different samples from the same object have some differences. In addition, the proposed NLDLSR is expanded to the kernel space, and we further propose a novel kernel noisy label based discriminative least squares regression algorithm (KNLDLSR). A large number of experiments show that our proposed algorithms can achieve very good performance.

• Journal of applied mathematics & informatics
• /
• 제34권1_2호
• /
• pp.95-106
• /
• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• 한국음향학회지
• /
• 제29권6호
• /
• pp.374-380
• /
• 2010

잡음이 섞인 입출력 신호를 갖는 시스템 인식 문제는 완전 최소 자승법 (Total Least Squares (TLS))으로 알려져 있다. 완전 최소 자승법의 성능은 입력 신호 부가 잡음 파워와 출력 신호 부가 잡음간의 분산비에 매우 민감하다. 본 논문에서는 TLS의 성능 향상을 위해서 LS (Least Squares)와의 결합을 제안한다. 그 한 형태로 재차적인 TLS (Recursive TLS)와 재차적인 LS (Recursive Least Squares)간의 결합 알고리즘을 제안한다. 이 결합은 잡음간 분산비에 강인한 결과를 낳았다. 모의실험을 통해 얻은 결과로부터 입력 신호에 신호대 잡음비가 5dB를 유지히는 잡음을 부가할 경우 입력 잡음과출력 잡음의 비 $\gamma$가 약 20 정도까지로 적용 범위가 확대되는 결과를 얻었다. 따라서 제안된 결합 방법이 기존의 TLS의 적용 범위를 넓힐 수 있음을 알 수 있다.