A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we estab...
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In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we establish the existence of solutions of the corresponding system of auxiliary variational inequalities problem. Then, using the existence result, we construct a new iterative algorithm. Finally, both the existence of solutions of the original problem and the convergence of iterative sequences generated by the algorithm are proved. We give an affirmative answer to the open problem raised by Noor et al. (Korean J. Comput. Appl. Math. 1:73-89, 1998;J. Comput. Appl. Math. 47:285-312, 1993). Our results improve and extend some known results.
In this article, we present an iterative self-training algorithm whose objective is to extend learners from a supervised setting into a semi-supervised setting. The algorithm is based on using the predicted values for...
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In this article, we present an iterative self-training algorithm whose objective is to extend learners from a supervised setting into a semi-supervised setting. The algorithm is based on using the predicted values for observations where the response is missing (unlabeled data) and then incorporating the predictions appropriately at subsequent stages. Convergence properties of the algorithm are investigated for particular learners, such as linear/logistic regression and linear smoothers with particular emphasis on kernel smoothers. Further, implementation issues of the algorithm with other learners such as generalized additive models, tree partitioning methods, partial least squares, etc. are also addressed. The connection between the proposed algorithm and graph-based semi-supervised learning methods is also discussed. The algorithm is illustrated on a number of real datasets using a varying degree of labeled responses.
Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T-1, T-2 : K -> E be two weakly inward and asymptotically nonexp...
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Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T-1, T-2 : K -> E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences {K-n},{l(n)} subset of [1,infinity), lim(n ->infinity) k(n) = 1, lim(n ->infinity) l(n) = 1, F(T-1) boolean AND F(T-2) = {x is an element of K : T(1)x = T(2)x = x} not equal empty set, respectively. Suppose that {x(n)} is a sequence in K generated iteratively by x(1) is an element of K, x(n+1) = alpha(n)x(n) + beta(n)(PT1)(n) x(n) + gamma(n)(PT2)(n) x(n), for all n >= 1, where {alpha(n)}, {beta(n)}, and {gamma(n)} are three real sequences in [epsilon, 1-epsilon] for some epsilon > 0 which satisfy condition alpha(n) + beta(n) + gamma(n) = 1. Then, we have the following. (1) If one of T-1 and T-2 is completely continuous or demicompact and Sigma(infinity)(n=1)(k(n) - 1) < infinity, Sigma(infinity)(n=1)(l(n) - 1) < infinity, then the strong convergence of {x(n)} to some q is an element of F(T-1) boolean AND F(T-2) is established. ( 2) If E is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Frechet differentiable, then the weak convergence of {x(n)} to some q is an element of F(T-1) boolean AND F(T-2) is proved.
In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get t...
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In this paper, we use the dual variable to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings in real Hilbert spaces. Under suitable conditions, we get the weak convergence of the proposed algorithm and give applications in the split feasibility problem and the split equality problem. Some numerical experiments are given to illustrate the efficiency of the proposed iterative algorithm. Our results improve and extend the corresponding results announced by many others.
In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration s...
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In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2].
A new system of generalized mixed implicity equilibrium problems is introduced and studied in real Banach spaces. The notion of the Yosida approximation introduced by Moudafi in Hilbert spaces is first generalized to ...
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A new system of generalized mixed implicity equilibrium problems is introduced and studied in real Banach spaces. The notion of the Yosida approximation introduced by Moudafi in Hilbert spaces is first generalized to reflexive Banach spaces. By using the notion of the Yosida approximation, a system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicity equilibrium problems is also proved. By using the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field.
In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem and the split equality fixed point problem of firmly quasi-nonexpansive mappings in real Hilbert spaces. Unde...
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In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem and the split equality fixed point problem of firmly quasi-nonexpansive mappings in real Hilbert spaces. Under very mild conditions, we prove a weak convergence theorem for our algorithm using projection method and the properties of firmly quasi-nonexpansive mappings. Our result improves and extends the corresponding ones announced by some others in the earlier and recent literature.
In this paper, we generalize the iterative scheme and extend the space studied in (Fixed Point Theory and Applications 2012: 46, 2012). Further, we prove some strong convergence theorems of the new iterative scheme fo...
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In this paper, we generalize the iterative scheme and extend the space studied in (Fixed Point Theory and Applications 2012: 46, 2012). Further, we prove some strong convergence theorems of the new iterative scheme for variational inequality problems in q-uniformly smooth Banach spaces under very mild conditions. Our results improve and extend corresponding ones announced by many others.
Strong H-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor. In this paper, first, an improved iterative algorithm is proposed to determine whether a given ...
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Strong H-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor. In this paper, first, an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor, and the validity of the iterative algorithm is proved theoretically. Second, the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor. Finally, numerical examples are presented to illustrate the advantages of the proposed algorithm.
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