comparisons of nonnegative splittings of matrices abstract the comparison of the asymptotic rates of convergence of two iteration matrices induced by two splitting of the same matrix has arisen in the work of many authors in this article some new comparison theorems for two nonnegative splittings a splitting a m n is nonnegative if m 1 exist and m 1 n is nonnegative are derived they extend the known results in the literature in addition we also point out three incorrect conditions in a paper by beauwens furthermore we give some reasonable conditions ensuring the strict inequality between the asymptotic convergence rates this also answers the open question which additional and appropriate conditions should be imposed on miller neumann splittings to obtain strict inequality finally some applications to a class of generalized aor sor and jor iterative methods whose special cases imply block also point aor sor and jor iterative methods for solving linear systems are discussed

an improved index of interactivity for fuzzy numbers in this paper we will introduce a new index of interactivity between marginal possibility distributions a and b of a joint possibility distribution c the starting point of our approach is to equip each c level set of c with a uniform probability distribution then the probabilistic correlation coefficient between its marginal probability distributions is interpreted as an index of interactivity between the c level sets of a and b then we define the index of interactivity between a and b as the weighted average of these indexes over the set of all membership grades this new index of interactivity is meaningful for the whole family of joint possibility distributions

random fuzzy variables of second order and applications to statistical inference abstract this paper summarizes some results on random fuzzy variables with existing expectation and variance called random fuzzy variables of second order using the frechet principle and via support functions the embedding of convex fuzzy sets into a banach space of functions it especially presents a unified view on expectation and variance of random fuzzy variables these notions are applied in developing linear statistical inference with fuzzy data detailed investigations are presented concerning best linear unbiased estimation in linear regression models with fuzzy observations

on possibilistic correlation in 2004 fuller and majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact based on this approach in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions moreover we will formulate the classical cauchy schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart in particular applying the idea of transforming level sets of possibility distributions into uniform probability distributions we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation

low complexity modem design for gfdm due to its attractive properties generalized frequency division multiplexing gfdm is recently being discussed as a candidate waveform for the fifth generation of wireless communication systems 5g gfdm is introduced as a generalized form of the widely used orthogonal frequency division multiplexing ofdm modulation scheme and since it uses only one cyclic prefix cp for a group of symbols rather than a cp per symbol it is more bandwidth efficient than ofdm in this paper we propose novel modem structures for gfdm by taking advantage of the particular structure in the modulation matrix our proposed transmitter is based on modulation matrix sparsification through application of fast fourier transform fft to reduce the implementation complexity a unified demodulator structure for matched filter mf zero forcing zf and minimum mean square error mmse receivers is also derived the proposed demodulation techniques harness the special block circulant property of the matrices involved in the demodulation stage to reduce the computational cost of the system implementation we have derived the closed forms for the zf and mmse receiver filters additionally our algorithms do not incur any performance loss as they maintain the optimal performance the computational costs of our proposed techniques are analyzed in detail and are compared with the existing solutions that are known to have the lowest complexity it is shown that through application of our structures a substantial amount of computational complexity reduction can be achieved

a note on comparison theorems for splittings and multisplittings of hermitian positive definite matrices abstract we discuss iterative methods for the solution of the linear system ax b which are based on a single splitting or a multisplitting of a in order to compare different methods it is common to compare the spectral radius of the iterative matrix for m matrices a and weak regular splittings there exist well known comparison theorems here we give a comparison theorem for splittings of hermitian positive definite matrices furthermore we establish a comparison theorem for multisplittings of a hermitian positive definite matrix

on the semiconvergence of additive and multiplicative splitting iterations for singular linear systems in this paper we investigate the additive multiplicative and general splitting iteration methods for solving singular linear systems when the coefficient matrix is hermitian the semiconvergence conditions are proposed which generalize some results of bai z z bai on the convergence of additive and multiplicative splitting iterations for systems of linear equations j comput appl math 154 2003 195 214 for the nonsingular linear systems to the singular systems

matrix characterization for gfdm low complexity mmse receivers and optimal filters in this paper a new matrix based characterization of generalized frequency division multiplexing gfdm transmitter matrices is proposed as opposed to traditional vector based characterization with prototype filters the characterization facilitates deriving properties of gfdm transmitter matrices including conditions for gfdm matrices being nonsingular and unitary respectively using the new characterization the necessary and sufficient conditions for the existence of a form of low complexity implementation for a minimum mean square error mmse receiver are derived such an implementation exists under multipath channels if the gfdm transmitter matrix is selected to be unitary for cases where this implementation does not exist a low complexity suboptimal mmse receiver is proposed with its performance approximating that of an mmse receiver the new characterization also enables derivations of optimal prototype filters in terms of minimizing receiver mean square error mse they are found to correspond to the use of unitary gfdm matrices under many scenarios the use of such optimal filters in gfdm systems does not cause the problem of noise enhancement thereby demonstrating the same mse performance as orthogonal frequency division multiplexing moreover we find that gfdm matrices with a size of power of two are verified to exist in the class of unitary gfdm matrices finally while the out of band oob radiation performance of systems using a unitary gfdm matrix is not optimal in general it is shown that the oob radiation can be satisfactorily low if parameters in the new characterization are carefully chosen

n continuous signaling for gfdm an n continuous generalized frequency division multiplexing gfdm transceiver architecture is studied with the objective of striking a balanced trade off between the bit error rate ber and the sidelobe suppression performance more specifically in the proposed n continuous gfdm signaling the basis signals constructed allow one to make the gfdm signal n continuous and attain a compact spectrum as an explicit benefit of sidelobe suppression we further reveal that compared to conventional n continuous orthogonal frequency division multiplexing nc ofdm n continuous gfdm introduces relatively low interference through evaluating the signal to interference ratio sir secondly a signal recovery algorithm is presented by constructing a recovery matrix to eliminate the interference finally it is demonstrated that the proposed n continuous gfdm scheme outperforms its n continuous ofdm counterpart in terms of sidelobe suppression while achieving moderate ber performance degradation as opposed to original ofdm

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

on interactive fuzzy numbers in this paper we will introduce a measure of interactivity between marginal distributions of a joint possibility distribution c as the expected value of the interactivity relation between the level sets of its marginal distributions

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

the convergence of linear stationary iterative processes for solving singular unstructured systems of linear equations this paper reviews the convergence properties of linear stationary iterative processes for solving large unstructured systems of linear equations special attention is given to the case where the system to be solved is singular and possibly inconsistent the review starts by investigating the iteration bf x k 1 h bf x k bf f k 0 1 2 cdots when the system i h bf x bf f is inconsistent in this case the sequence left bf x k right always diverges nevertheless when h is convergent there exists a vector bf q in text null i h such that the sequence hat bf x k bf x k k bf q converges the limit of this sequence hat bf x solves a certain least squares problem and the sequence of residual vectors bf r k i h bf x k bf f converges to i h hat bf x bf f furthermore if h is similar to a real diagonal matrix then the corresponding norms of bf r k and hat bf x k hat bf x decr

a subjective approach for ranking fuzzy numbers abstract starting from a subjective assignation of weights related to the relative importance of the different level sets we define a new method of comparison of fuzzy numbers this procedure is an extension of some well known indices adamo tsumura et al yager some properties of our index are studied in this paper as well as its behaviour on several particular cases

optimal orthogonal precoding for power leakage suppression in dft based systems a solution to the power leakage minimization problem in discrete fourier transform dft based communication systems is presented in a conventional dft based system modulated subcarriers exhibit high sidelobe levels which leads to significant out of band power leakage existing techniques found in the literature either do not achieve sufficient sidelobe suppression or suffer from significant spectral efficiency loss precoding can be seen as a general linear processing method for power leakage reduction however how to design the optimal linear precoder is still an open problem in this paper the power leakage suppression is first treated as a matrix frobenius norm minimization problem and then the optimal orthogonal precoding matrix design for the power leakage suppression is proposed based on singular value decomposition svd by further exploiting the extra degrees of freedom in the precoding matrix two kinds of optimized precoding matrices one with multi carrier property and the other with single carrier property are developed to take the advantages of orthogonal frequency division multiplexing ofdm and single carrier frequency division multiple access sc fdma respectively simulation results show that both the multi carrier and the single carrier precoding schemes achieve significant power leakage suppression and have similar peak to average power ratio papr and bit error rate ber to those of ofdm and sc fdma systems respectively

theorems on m splittings of a singular m matrix which depend on graph structure abstract let a m ne r n n be a splitting we investigate the spectral properties of the iteration matrix m 1n by considering the relationships of the graphs of a m n and m 1n we call a splitting an m splitting if m is a nonsingular m matrix and n 0 for an m splitting of an irreducible z matrix a we prove that the circuit index of m 1n is the greatest common divisor of certain sets of integers associated with the circuits of a for m splittings of a reducible singular m matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting these results hold under somewhat weaker assumptions

on parallel multisplitting block iterative methods for linear systems arising in the numerical solution of euler equations the paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of euler equations some sufficient conditions for convergence are proposed as special cases the convergence of the parallel block generalized aor bgaor the parallel block aor baor the parallel block generalized sor bgsor the parallel block sor bsor the extrapolated parallel baor and the extrapolated parallel bsor methods are presented furthermore the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of euler equations are discussed finally some examples are given to demonstrate the convergence results obtained in this paper

on parallel multisplitting iterative methods for singular linear systems in this paper the semiconvergence of parallel multisplitting iterative methods and extrapolated parallel methods for singular linear systems is discussed some sufficient conditions for semiconvergence are presented whenever the multisplittings are p regular sub regular or nonnegative as special cases the semiconvergence of parallel generalized aor block aor aor parallel generalized sor block sor sor extrapolated parallel generalized block aor and extrapolated parallel generalized block sor methods are proved

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

semiconvergence of extrapolated iterative methods for singular linear systems abstract in this paper we discuss convergence of the extrapolated iterative methods for solving singular linear systems a general principle of extrapolation is presented the semiconvergence of an extrapolated method induced by a regular splitting and a nonnegative splitting is proved whenever the coefficient matrix a is a singular m matrix with property c and an irreducible singular m matrix respectively since the generalized block jor and aor methods are respectively the extrapolated methods of the generalized block jacobi and sor methods so the semiconvergence of the generalized block jor and aor methods for solving general singular systems are proved furthermore the semiconvergence of the extrapolated power method the block jor aor and sor methods for solving markov chains are discussed

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1