The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to r...
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The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds.
In the paper, first, we introduce a new hybrid projection algorithm and present its strong convergence theorem. Next, we analyze different hybrid algorithms in computing and conclude that our proposed algorithm has an...
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In the paper, first, we introduce a new hybrid projection algorithm and present its strong convergence theorem. Next, we analyze different hybrid algorithms in computing and conclude that our proposed algorithm has an advantage. Finally, the numerical experiments validate the efficiency and advantages of the new algorithm.
In many radar applications, including marine, automotive and MIMO, there is a need for orthogonal transmission from different radar sets to mitigate mutual interference;the same applies to the different channels in a ...
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ISBN:
(纸本)9788377981603
In many radar applications, including marine, automotive and MIMO, there is a need for orthogonal transmission from different radar sets to mitigate mutual interference;the same applies to the different channels in a MIMO radar. New techniques, belonging to the cyclic algorithm family, might be used to generate orthogonal signals with, in addition, low sidelobes in their autocorrelation function in order to mitigate both interference and masking effects due to dynamic range problem. Their performance analysis is shown.
Let E be a real 2-uniformly smooth Banach space which is also uniformly convex (for example: L-p or l(P), 2 K be strictly pseudocontractive mappings of K into K in the sense of Browder and Petryshyn with boolean AND(...
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Let E be a real 2-uniformly smooth Banach space which is also uniformly convex (for example: L-p or l(P), 2 <= p < infinity) and K a nonempty closed convex subset of E. Let T-1, T-2,T-..., T-N : K -> K be strictly pseudocontractive mappings of K into K in the sense of Browder and Petryshyn with boolean AND(N)(i=1) F(T-i) not equal empty set, where F(T-i) = {x is an element of K : T(i)x = x). Let {alpha(n)}(n=1)(infinity) be a real sequence in [0,1] satisfying the condition 0 < a <= (1 - alpha(n)) <= b < 2 lambda/c, for all n >= 1 and for some constants, a, b, lambda is an element of (0, 1) and c >= 1. Let {x(n)} be the sequence generated from an arbitrary x(1) is an element of K by x(n+1) = alpha(n)x(n) + (1 - alpha(n)) T(vertical bar n vertical bar)x(n), n >= 1 where T-vertical bar n vertical bar = T-i, i = n (mod N), 1 <= i <= N. Weak and strong convergence theorems for the iterative approximation of common fixed points of the family (T-i}(i=1)(N) are proved using the iterative sequence {x(n)}(n=1)(infinity). Furthermore, if E is an arbitrary real Banach space, it is shown that lim inf(n ->infinity) parallel to x(n)-T(i)x(n)parallel to = 0 for all i = 1, 2,.... N;and a necessary and sufficient condition that guarantees the strong convergence of {x(n)} to a common fixed point of the family {T-i} is given. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, we study synchronal and cyclic algorithms for finding a common fixed point x* of a finite family of strictly pseudocontractive mappings, which solve the variational inequality = 1 is a positive integer,...
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In this paper, we study synchronal and cyclic algorithms for finding a common fixed point x* of a finite family of strictly pseudocontractive mappings, which solve the variational inequality <(gamma f - mu G)x*, j(q)(x - x*) <= 0, for all x is an element of boolean AND F-N(i=1)(T-i), where f is a contraction mapping, G is an eta-strongly accretive and L-Lipschitzian operator, N >= 1 is a positive integer, gamma, mu > 0 are arbitrary fixed constants, and {T-i}(i=1)(N) are N-strict pseudocontractions. Furthermore, we prove strong convergence theorems of such iterative algorithms in a real q-uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
The cybernetic approach is used to develop a mathematical model for communicating queuing systems. Conflicting input flows of the first queuing system and one of the input flows of the second queuing system are formed...
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The cybernetic approach is used to develop a mathematical model for communicating queuing systems. Conflicting input flows of the first queuing system and one of the input flows of the second queuing system are formed in a synchronous Markov random environment with a finite number of states. Another input flow of the second queuing system consists of retrials arriving from the first queuing system. The transition of a customer from the first queuing system to the second one takes a random amount of time. Servicing is performed by a cyclic algorithm with fixed duration.
Sequences with impulse-like correlations are at the core of several radar and communication applications. Two criteria that can be used to design such sequences, and which lead to rather different results in the aperi...
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Sequences with impulse-like correlations are at the core of several radar and communication applications. Two criteria that can be used to design such sequences, and which lead to rather different results in the aperiodic correlation case, are shown to be identical in the periodic case. Furthermore, two simplified versions of these two criteria, which similarly yield completely different sequences in the aperiodic case, are also shown to be equivalent. A corollary of these unexpected equivalences is that the periodic correlations of an arbitrary sequence must satisfy an intriguing identity, which is also presented in this letter.
A multi-input multi-output (MIMO) radar system, unlike a standard phased-array radar, can transmit multiple probing signals that are correlated or uncorrelated with each other. This waveform diversity offered by the M...
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ISBN:
(纸本)9781424415380
A multi-input multi-output (MIMO) radar system, unlike a standard phased-array radar, can transmit multiple probing signals that are correlated or uncorrelated with each other. This waveform diversity offered by the MIMO radar is the main reason for its superiority over the standard phased-array radar. An interesting current research topic in MIMO radar is the optimal synthesis of the transmitted waveforms. Recently proposed techniques for MIMO radar waveform synthesis have focused on the optimization of the covariance matrix R of the waveforms, as optimizing a performance metric directly with respect to the waveform matrix is a more complicated operation. Given an R, the problem becomes that of determining a signal waveform matrix X whose covariance matrix is equal or close to K and which also satisfies some practically motivated constraints. We propose a cyclic optimization algorithm for the synthesis of such an X, which (approximately) realizes a given optimal covariance matrix R under various practical constraints, and which also has good auto- and cross- correlation properties in time, if desired. A number of numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
Let {T-i}(i = 1)(N) be N strict pseudo-contractions defined on a closed convex subset C of a real Hilbert space H. Consider the problem of finding a common fixed point of these mappings and consider the parallel and c...
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Let {T-i}(i = 1)(N) be N strict pseudo-contractions defined on a closed convex subset C of a real Hilbert space H. Consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms. Moreover, by applying additional projections, we further prove that these algorithms can be modified to have strong convergence. (C) 2006 Elsevier Ltd. All rights reserved.
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