verified solution of large systems and global optimization problems recent results on the solution of large banded or sparse systems and on global unconstrained optimization problems including verification of the correctness of the result will be discussed the computing time for the verification for large linear systems is the same as for the decomposition the total computational effort for verifying the global optimum value is for well known test examples competitive to those of pure floating point algorithms computational examples will be demonstrated

robust switching output feedback control of time varying polytopic uncertain systems abstractthe problem of designing a globally optimal robust output feedback controller for time varying polytopic uncertain systems is a well known non convex optimisation problem in this paper new sufficient conditions for both robust h2 and h switching output feedback control syntheses are proposed in terms of bilinear matrix inequalities bmis under the multiple lyapunov function framework this set of synthesis conditions is further reduced to a special type of bmis which can be solved effectively using linear matrix inequality optimisation plus a line search the associated robust output feedback controller is constructed as a switching type full order dynamic output feedback controller consisting of a family of linear time invariant subcontrollers and a min switching logic the proposed approach features the important property of computational efficiency with stringent performance its effectiveness and advantages have been demonstrated through extensive numerical studies

numerical verification of solutions for a simplified signorini problem abstract we proposed some numerical methods for the automatic proof of existence of solutions for variational inequalities i e obstacle problems and elastoplastic torsion problems it is based on nakao s method by using finite element approximation and its explicit error estimates for the problem in this paper we present a numerical verification algorithm of exact solutions for a simplified signorini problem in a computer a numerical example for the signorini problem is presented

a framework of verified eigenvalue bounds for self adjoint differential operators for eigenvalue problems of self adjoint differential operators a universal framework is proposed to give explicit lower and upper bounds for the eigenvalues in the case of the laplacian operator by applying crouzeix raviart finite elements an efficient algorithm is developed to bound the eigenvalues for the laplacian defined in 1d 2d and 3d spaces moreover for nonconvex domains for which case there may exist singularities of eigenfunctions around re entrant corners the proposed algorithm can easily provide eigenvalue bounds by further adopting the interval arithmetic the explicit eigenvalue bounds from numerical computations can be mathematically correct

an enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems abstract we consider eigenvalue enclosing of the elliptic operator which is linearized at an exact solution of certain nonlinear elliptic equation this problem is important in the mathematically rigorous analysis of the stability or bifurcation of some solutions for nonlinear problems we formulate such a kind of eigenvalue problem as the nonlinear system which contains both linearized eigenvalue problem and the original nonlinear equation we also consider the indices of eigenvalues especially the first eigenvalue of such a problem in these enclosing procedures the finite dimensional verified computations for linear and nonlinear system of equations play an essential role a numerical example is presented

the fast hartley transform algorithm the fast hartley transform fht is similar to the cooley tukey fast fourier transform fft but performs much faster because it requires only real arithmetic computations compared to the complex arithmetic computations required by the fft through use of the fht discrete cosine transforms dct and discrete fourier transforms dft can be obtained the recursive nature of the fht algorithm derived in this paper enables us to generate the next higher order fht from two identical lower order fht s in practice this recursive relationship offers flexibility in programming different sizes of transforms while the orderly structure of its signal flow graphs indicates an ease of implementation in vlsi

an analysis of real fourier domain based adaptive algorithms implemented with the hartley transform using cosine sine symmetries the least mean squared lms algorithm and its variants have been the most often used algorithms in adaptive signal processing however the lms algorithm suffers from a high computational complexity especially with large filter lengths the fourier transform based block normalized lms fbnlms reduces the computation count by using the discrete fourier transform dft and exploiting the fast algorithms for implementing the dft even though the savings achieved with the fbnlms over the direct lms implementation are significant the computational requirements of fbnlms are still very high rendering many real time applications like audio and video estimation infeasible the hartley transform based bnlms hbnlms is found to have a computational complexity much less than and a memory requirement almost of the same order as that of the fbnlms this paper is based on the cosine and sine symmetric implementation of the discrete hartley transform dht which is the key in reducing the computational complexity of the fbnlms by 33 asymptotically with respect to multiplications the parallel implementation of the discrete cosine transform dct in turn can lead to more efficient implementations of the hbnlms

on computing the split radix fft this paper presents an efficient fortran program that computes the duhamel hollmann split radix fft an indexing scheme is used that gives a three loop structure for the split radix fft that is very similar to the conventional cooley tukey fft both a decimation in frequency and a decimation in time program are presented an arithmetic analysis is made to compare the operation count of the cooley tukey fft fo several different radixes to that of the split radix fft the split radix fft seems to require the least total arithmetic of any power of two dft algorithm

numerical verification of solutions for some unilateral boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for some unilateral boundary value problems using the finite element approximations and explicit a priori error estimates we construct in a computer a set of solutions which satisfies the hypothesis of schauder s fixed point theorem for a compact map on a certain sobolev space further the conditions of verifiability by this method are considered and some numerical examples are presented

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

fractional cosine sine and hartley transforms in previous papers the fourier transform ft has been generalized into the fractional fourier transform frft the linear canonical transform lct and the simplified fractional fourier transform sfrft because the cosine sine and hartley transforms are very similar to the ft it is reasonable to think they can also be generalized by the similar way we introduce several new transforms they are all the generalization of the cosine sine or hartley transform we first derive the fractional cosine sine and hartley transforms frct frst frht they are analogous to the frft then we derive the canonical cosine and sine transforms cct cst they are analogous to the lct we also derive the simplified fractional cosine sine and hartley transforms sfrct sfrst sfrht they are analogous to the sfrft and have the advantage of real input real output we also discuss the properties digital implementation and applications e g the applications for filter design and space variant pattern recognition of these transforms the transforms introduced in this paper are very efficient for digital implementation we can just use one half or one fourth of the real multiplications required for the frft and lct to implement them when we want to process even odd or pure real imaginary functions we can use these transforms instead of the frft and lct besides we also show that the frct frst cct cst and sfrct sfrst are also useful for the one sided t spl isin 0 spl infin signal processing

a numerical verification method for solutions of boundary value problems with local uniqueness by banach s fixed point theorem in this paper we propose a method to prove the existence and the local uniqueness of solutions to infinite dimensional fixed point equations using computers choosing a set which possibly includes a solution we transform it by an approximate linearization of the operator appearing in the equation then we calculate the radii of the transformed set in order to check sufficient conditions for banach s fixed point theorem this method is applied to elliptic problems and numerical examples are given

suboptimal switching control consistency analysis for switched linear systems this paper introduces the concept of consistency for continuous time switched linear systems having the switching function as a primary control signal to be designed a switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems conditions under which a min type switching strategy is strictly consistent for the classes of h2 and h performance indexes are determined this property makes clear the importance of switching systems control design in both theoretical and practical application frameworks moreover with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed the theory is illustrated by means of several academic examples

a generalized approach to direction finding with reference to the recently developed estimation of signal parameters using a rotational invariance techniques esprit it is pointed out that other operators can be used to generate the matrix pencil by way of example the moving window operator is discussed

fast hartley transform pruning the discrete hartley transform dht is discussed as a tool for the processing of real signals fast hartley transform fht algorithms which compute the dht in a time proportional to n log sub 2 n exist in many applications such as interpolation and convolution of signals a significant number of zeros are padded to the nonzero valued samples before the transform is computed it is shown that for such situations significant savings in the number of additions and multiplications can be obtained by pruning the fht algorithm the modifications in the fht algorithm as a result of pruning are developed and implemented in an fht subroutine the amount of savings in the operation is determined

numerical verification of solutions for obstacle problems this article is an extension of the previous paper numer math 81 1998 305 by the same authors we propose a method to prove the existence of solutions for more general obstacle problems by numerical computations the main task in this paper consists of the numerical determination of some constants which appear in a priori error estimations for the finite element approximation of a simple variational inequality we present a numerical example for verification

a computer assisted proof for the kolmogorov flows of incompressible viscous fluid a computer assisted proof of non trivial steady state solutions for the kolmogorov flows is described the method is based on the infinite dimensional fixed point theorem using newton like operator this paper also proposes a numerical verification algorithm which generates automatically on a computer a set including the exact non trivial solution with local uniqueness all discussed numerical results take into account the effects of rounding errors in the floating point computations

brief paper dynamic output feedback h control of switched linear systems this paper is devoted to dynamic output feedback h control design of switched linear systems in both continuous and discrete time domains more specifically the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed loop switched linear system globally asymptotically stable and impose a pre specified upper bound to the l 2 gain an example of practical importance is presented to illustrate the validity and efficiency of the theory

stability analysis of lur e type switched systems this technical note aims to introduce stability analysis of lur e type switched systems in frequency domain a new state input dependent switching function is proposed and it is the key issue to obtain a stability condition that generalizes the celebrated popov criterion to deal with this class of switched nonlinear systems likewise the case of time invariant systems we propose a frequency domain stability test that is expressed through a convex combination of the subsystems state space matrices this task is not trivial due to the time varying nature of the nonlinear systems under consideration the theory is illustrated by a simple example

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

fast computation of the discrete cosine transform and the discrete hartley transform a new factorization of the discrete hartley transform dht is presented it is used to derive new algorithms for the dht and the discrete cosine transform dct with reduced number of multiplications

numerical verification of solutions for obstacle problems using a newton like method abstract this paper is a continuation of the preceding study 1 in which we described a method which automatically proves the existence of solutions for variational inequalities by computer we newly formulate a verification method using a newton like method this approach enables us to remove the restriction in the previous paper to the retraction property of the operator in a neighborhood of the solution we show some numerical examples which confirm that the method is really applicable to problems which have no retraction property

the vector split radix algorithm for 2d dht a decimation in frequency vector split radix algorithm is proposed to decompose an n n 2d discrete hartley transform dht into one n 2 n 2 dht and twelve n 4 dhts the proposed algorithm possesses the in place property and needs no matrix transpose its computational structure is very regular and is simpler than those of all existing nonseparable 2d dhts

on computational proofs of the existence of solutions to nonlinear parabolic problems abstract this paper is an extension of the preceding study nakao this journal 1991 in which we described a numerical verification method of the solution for one space dimensional parabolic problems to the several space dimensional case here numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer we reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed point problem of a compact operator on certain function spaces as in the preceding study based upon a simple c 0 finite element approximation and its constructive a priori error estimates a numerical verification procedure is presented with some numerical examples

unified parallel lattice structures for time recursive discrete cosine sine hartley transforms unified efficient computations of the discrete cosine transform dct discrete sine transform dst discrete hartley transform dht and their inverse transforms employing the time recursive approach are considered unified parallel lattice structures that can dually generate the dct and dst simultaneously as well the dht are developed these structures can obtain the transformed data for sequential input time recursively with a throughput rate of one per clock cycle the total number of multipliers required is a linear function of the transform size n with no constraint on n the resulting architectures are regular modular and without global communication so that they are very suitable for vlsi implementation for high speed applications it is shown that the dct dst dht and their inverse transforms share an almost identical lattice structure the tradeoff between time and area for the block data processing is considered

hartley transforms over finite fields a general framework is presented for constructing transforms in the field of the input which have a convolution like property the construction is carried out over finite fields but is shown to be valid over the real and complex fields as well it is shown that these basefield transforms can be viewed as projections of the discrete fourier transform dft and that they exist for all lengths n for which the dft is defined the convolution property of the basefield transforms is derived and a condition for such transforms to have the self inverse property is given also fast algorithms for these basefield transforms are developed showing gains when compared to computations using the fft application of the methodology to hartley transforms over r leads to a simple derivation of fast algorithms for computing real hartley transforms

technical communique switched state feedback control for continuous time uncertain systems this paper is concerned to design a switched state feedback robust control for continuous time systems subject to norm bounded uncertainty as important features of the proposed design method we mention that it can handle a general lft structure for the uncertainty and it is based on stability conditions that can be numerically solved by means of lmis and a line search moreover the switching rule as well as the state feedback gains are determined from the minimization of a guaranteed cost function derived from a multi objective criterion the theoretical results are illustrated with an academic example

on the two dimensional vector split radix fft algorithm the complete equations are presented for the first stage of the two dimensional vector split radix decimation in frequency fast fourier transform algorithm using a structural approach the computational complexity of the algorithm is discussed and compared to other published results the author states that generally the vector split radix method provides a significant reduction in the number of complex multiplications required to implement a two dimensional discrete fourier transform

improved fourier and hartley transform algorithms application to cyclic convolution of real data this paper highlights the possible tradeoffs between arithmetic and structural complexity when computing cyclic convolution of real data in the transform domain both fourier and hartley based schemes are first explained in their usual form and then improved either from the structural point of view or in the number of operations involved namely we first present an algorithm for the in place computation of the discrete fourier transform on real data a decimation in time split radix algorithm more compact than the previously published one second we present a new fast hartley transform algorithm with a reduced number of operations a more regular convolution scheme based on fft s is also proposed finally we show that hartley transforms belong to a larger class of algorithms characterized by their generalized convolution property

assessing the hartley transform the fast algorithm for the real hartly transform is discussed in relation to the established fast algorithm for the complex fourier transform the two transforms are compared by timing comparably written programs on a given machine and the discipline of timing is discussed as an adjunct to complexity analysis with real data one hartley transform program can economically replace such packages as a complex valued unilateral fourier transform combined with a real valued unilateral inverse fourier transform the hartley transform is favorable for fast convolution of real data sets the utility of spectral analysis into fourier series throughout physics suggested that the hartley transform might have less physical significance but the construction of hartley diffraction planes in the microwave and optical laboratories where electromagnetic phase is encoded as real valued field amplitudes has revealed interesting complementarity

numerical verification of solutions for variational inequalities in this paper we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities this technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations using the finite element approximations and explicit a priori error estimates for obstacle problems we present an effective verification procedure that through numerical computation generates a set which includes the exact solution further a numerical example for an obstacle problem is presented

an efficient numerical verification method for the kolmogorov problem of incompressible viscous fluid some computer assisted proofs of nontrivial steady state solutions for the kolmogorov flows are presented the method is based on the infinite dimensional fixed point theorem using a newton like operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution when discussing the numerical results we consider the effects of rounding errors in the floating point computations this is a continuation of our study that was presented in watanabe 2009

improved synthesis conditions for mixed h2 h gain scheduling control subject to uncertain scheduling parameters abstractthe vast majority of the existing work in gain scheduling gs control literature assumes perfect knowledge of scheduling parameters generally this assumption is not realistic since for practical control applications measurement noises are unavoidable in this paper novel synthesis conditions are derived to synthesise robust gs controllers with mixed h2 h performance subject to uncertain scheduling parameters the conditions are formulated in terms of parameterised bilinear matrix inequalities pbmis that depend on varying parameters inside multi simplex domain the conditions provide practical gs controllers independent of the derivatives of scheduling parameters that is the designed controllers are feasible for implementation since bilinear matrix inequality problems are intractable an iterative pbmi algorithm is developed to solve the developed synthesis conditions by the virtue of this algorithm conservativeness reduction is achieved with few iterations examples are presented to il

implementation of split radix fft algorithms for complex real and real symmetric data a new algorithm is presented for the fast computation of the discrete fourier transform this algorithm belongs to that class of recently proposed 2n fft s which present the same arithmetic complexity the lowest among any previously published one moreover this algorithm has the advantage of being performed in place by repetitive use of a butterfly type structure without any data reordering inside the algorithm furthermore it can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm

algorithms meeting the lower bounds on the multiplicative complexity of length 2 sup n dfts and their connection with practical algorithms in a previous work see electron lett vol 20 no 17 p 690 1984 the author described an algorithm that computes a length 2 sup n discrete fourier transform using 2 sup 2 1 2n sup 2 4n 8 nontrivial i e not or j or square root 1 complex multiplications in the present work it is first shown that this algorithm actually provides the attainable lower bound on the number of complex multiplications a slight modification of the last step of this algorithm is also shown to provide the attainable lower bound on the number of real multiplications a connection with the split radix fft algorithm srfft is then explained showing that srfft is another variation of these optimal algorithms where the last step is computed recursively from shorter ffts in a suboptimal manner finally once the connection between the minimal complexity and srfft which is the best known practical algorithm is understood it provides useful information on the possibility of further improvements of the srfft

numerical verifications of solutions for elliptic equations in nonconvex polygonal domains in this paper methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied in order to verify solutions using computer it is necessary to determine some constants which appear in a priori error estimations we propose some methods for determination of these constants in numerical examples calculating these constants for anl shaped domain we verify the solution of a nonlinear elliptic equation

a comment on on prime factor mapping for the discrete hartley transform lun and sin see ieee trans signal processing vol 40 no 6 p 1399 1411 1982 describe a method of computing prime factor decomposed discrete hartley transform dht over n points with 2n less additions compared to the existing algorithms of bracewell and sorensen 1976 the author shows how the method of lun and siu ran be extended to eliminate the 2n extra additions in the algorithms of bracewell and sorenson

constructive a priori error estimates for a full discrete approximation of the heat equation in this paper we consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation our method is based on the finite element galerkin method with an interpolation in time that uses the fundamental solution for semidiscretization in space the present estimates play an essential role in the numerical verification method of exact solutions for the nonlinear parabolic equations this implies that by utilizing the present results we could get the guaranteed a posteriori error estimates for various kinds of nonlinear evolutional problems our results can also be considered as an explicit optimal estimate with the limited regularity of solutions which should be unknown up to the present

radix 2 spl times 2 spl times 2 algorithm for the 3 d discrete hartley transform the discrete hartley transform dht has proved to be a valuable tool in digital signal image processing and communications and has also attracted research interests in many multidimensional applications although many fast algorithms have been developed for the calculation of one and two dimensional 1 d and 2 d dht the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention hence the multidimensional hartley transform is usually calculated through the row column approach however proper multidimensional algorithms can be more efficient than the row column method and need to be developed therefore it is the aim of this paper to introduce the concept and derivation of the three dimensional 3 d radix 2 spl times 2 spl times 2 algorithm for fast calculation of the 3 d discrete hartley transform the proposed algorithm is based on the principles of the divide and conquer approach applied directly in 3 d it has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row column approach based on similar algorithms

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element the verifications of solutions to weakly nonlinear elliptic equations by the method described e g by nakao 1988 1989 etc are sometimes hardly accomplished when the right hand sides of the equations are very large to overcome such difficulties a residual iteration technique with approximate solution was introduced by nakao 1993 in the present paper we propose an a posteriori method for the residual iteration and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element

on computing the discrete hartley transform the discrete hartley transform dht is a real valued transform closely related to the dft of a real valued sequence bracewell has recently demonstrated a radix 2 decimation in time fast hartley transform fht algorithm in this paper a complete set of fast algorithms for computing the dht is developed including decimation in frequency radix 4 split radix prime factor and winograd transform algorithms the philosophies of all common fft algorithms are shown to be equally applicable to the computation of the dht and the fht algorithms closely resemble their fft counterparts the operation counts for the fht algorithms are determined and compared to the counts for corresponding real valued fft algorithms the fht algorithms are shown to always require the same number of multiplications the same storage and a few more additions than the real valued fft algorithms even though computation of the fht takes more operations in some situations the inherently real valued nature of the discrete hartley transform may justify this extra cost

a posteriori error bounds for two point boundary value problems consider a general two point boundary value problem tpbvp begin gathered y t f t y hfill b 1 y a b 2 y b w quad hfill end gathered a leqq t leqq b where f r n 1 to r n f in c 2 b 1 and b 2 are n times n matrices and w in r n it is shown how one can bound a posteriori the error made in the numerical solution of the tpbvp the error bounds obtained are rigorous and include the truncation and the roundoff error in addition the computations establish the existence of solutions to the tpbvp numerical schemes are developed for the case where f t y is a polynomial in t and y examples are given of computational existence proofs for problems where analytical existence proofs are not known

on very accurate enclosure of the optimal constant in the a priori error estimates for h02 projection we present constructive a priori error estimates for h 0 2 projection into a space of polynomials on a one dimensional interval here constructive indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form using the properties of legendre polynomials we consider a method by which to determine these constants to be as small as possible using the proposed technique the optimal constant could be enclosed in a very narrow interval with result verification furthermore constructive error estimates for finite element h 0 2 projection in one dimension are presented these types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method e g hashimoto et al 2006 2 nakao et al 2008 3 watanabe et al 2009 11

dynamic output feedback control of switched linear systems this paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete time domains a particular class of matrix inequalities the so called lyapunov metzler inequalities provides conditions for open loop stability analysis and closed loop switching control using state and output feedback switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the hamilton jacobi bellman inequality an upper bound on the optimal cost associated with a closed loop stabilizing switching strategy is provided as well the solution of the output feedback problem is based on the construction of a full order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule throughout the theoretical results are illustrated by means of academic examples a realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported

a prime factor fast w transform algorithm a method for converting any nesting dft algorithm to the type i discrete w transform dwt i is introduced a nesting algorithm that differs from either the windograd fourier transform algorithm wfta or the prime factor fft algorithm pfa is presented new small n dets which are suitable for this nesting algorithm are developed based on using sparse matrix decomposition the proposed algorithm is more efficient that either wfta or pfa for large n and it is more flexible for the choice of transform length because 32 points are used for 2d processing the proposed algorithm is more efficient than the polynomial transform

a numerical approach to the proof of existence of solutions for some generalized obstacle problems in 8 we proposed some numerical verification methods for automatic proof of the existence of solution for obstacle problems in this paper we propose a new iterative algorithm to automatically prove the existence of solutions for some generalized obstacle problems

numerical verification of solutions for elasto plastic torsion problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for the elasto plastic torsion problems governed by the variational inequality based upon the finite element approximations and the explicit a priori error estimates for a simple problem we present an effective verification procedure that through numerical computation generates a set which includes the exact solution this paper is an extension of the previous paper 1 in which we mainly dealt with the obstacle problems but some special techniques are utilized to verify the solutions for nondifferentiable nonlinear equations concerned with the present problem a numerical example is illustrated

stabilization and robust h control for sector bounded switched nonlinear systems this paper presents stability analysis and robust h control for a particular class of switched systems characterized by nonlinear functions that belong to sector sets with arbitrary boundaries the sector boundaries can have positive and or negative slopes and therefore we cover the most general case in our approach using the special structure of the system but without making additional assumptions e g on the derivative of the nonlinear functions and by proposing new multiple lyapunov function candidates we formulate stability conditions and a control design procedure in the form of matrix inequalities the proposed lyapunov functions are more general than the quadratic functions previously proposed in the literature as they incorporate the nonlinearities of the system and hence lead to less conservative stability conditions the stabilizing switching controllers are designed through a bi level optimization problem that can be efficiently solved using a combination of a convex optimization algorithm and a line search method the proposed optimization problem is achieved using a special loop transformation to normalize the arbitrary sector bounds and by other linear matrix inequalities lmi techniques

split radix fast hartley transform in one and two dimensions a simple matrix decomposition is provided as a derivation of the one dimensional split radix fast hartley transform fht the method is then extended in a straightforward manner to the two dimensional fht 2 d fht by implementing the vector radix approach as a result the proposed algorithm requires many fewer computational operations than the nonsplit vector radix 2 d fht method

verified eigenvalue evaluation for the laplacian over polygonal domains of arbitrary shape the finite element method fem is applied to bound leading eigenvalues of the laplace operator over polygonal domains compared with classical numerical methods most of which can only give concrete eigenvalue bounds over special domains of symmetry our proposed algorithm can provide concrete eigenvalue bounds for domains of arbitrary shape even when the eigenfunction has a singularity the problem of eigenvalue estimation is solved in two steps first we construct a computable a priori error estimation for the fem solution of poisson s problem which holds even for nonconvex domains with reentrant corners second new computable lower bounds are developed for the eigenvalues because the interval arithmetic is implemented throughout the computation the desired eigenvalue bounds are expected to be mathematically correct we illustrate several computation examples such as the cases of an l shaped domain and a crack domain to demonstrate the efficiency and flexibility of the proposed method

structured fast hartley transform algorithms the flowgraph originally proposed for the computation of the radix 2 fast hartley transform fht is restructured for clarity and ease of implementation with hardware and software by applying the transposition theorem to the newly formed flowgraph which corresponds to a decimation in time algorithm a decimation in frequency algorithm with a similar flowgraph is obtained the number of operations for the two algorithms is the same because of an existing symmetry which is also identical to that of another fht algorithm recently proposed

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

fast dht algorithms for length n q 2 sup m this article presents an improved split radix algorithm that can flexibly compute the discrete hartley transforms dht of length q 2 sup m where q is an odd integer comparisons with previously reported algorithms show that savings on the number of arithmetic operations can be made furthermore a wider range of choices on different dht lengths is naturally provided

numerical verification of solutions for signorini problems using newton like method we proposed a numerical method to verify the existence of solutions for a simplified signorini problem comput math appl 2000 40 1003 1013 using sequential iteration method we numerically constructed a set containing solutions that satisfies the hypothesis of schauder s fixed point theorem in a certain sobolev space it is difficult to apply this method to the problem of which associated operator is not retractive in a neighborhood of the solution in this paper in order to overcome such a difficulty we describe an alternative approach to this problem numerical examples are presented copyright 2007 john wiley sons ltd

an efficient prime factor algorithm for the discrete cosine transform and its hardware implementations the prime factor decomposition is a fast computational technique for many important digital signal processing operations such as the convolution the discrete fourier transform the discrete hartley transform and the discrete cosine transform dct the authors present a new prime factor algorithm for the dct they also design a prime factor algorithm for the discrete sine transform based on the prime factor dct algorithm hardware implementations for the prime factor dct are also studied they are especially interested in the hardware designs which are suitable for the vlsi implementations they show three hardware designs for the prime factor dct including a vlsi circuit fabricated directly according to the signal flow graph a linear systolic array and a mesh connected systolic array these three designs show the trade off between cost and performance the methodology which deals with general n sub 1 spl times n sub 2 point dcts where n sub 1 and n sub 2 are mutually prime is illustrated by converting a 15 point dct problem into a 3 spl times 5 point 2d dct problem

numerical verification of solutions for nonlinear elliptic problems using anl residual method abstract we consider a numerical enclosure method with guaranteedl error bounds for the solution of nonlinear elliptic problems of second order by using an a posteriori error estimate for the approximate solution of the problem with a higher orderc0 finite element it is shown that we can obtain the guaranteedl error bounds with high accuracy a particular emphasis is that our method needs no assumption of the existence of the solution of the original nonlinear equation but it follows as the result of computation itself a numerical example that confirms the effectiveness of the method is presented

a new class of quasi newtonian methods for optimal learning in mlp networks in this paper we present a new class of quasi newton methods for an effective learning in large multilayer perceptron mlp networks the algorithms introduced in this work named lqn utilize an iterative scheme of a generalized bfgs type method involving a suitable family of matrix algebras l the main advantages of these innovative methods are based upon the fact that they have an o nlogn complexity per step and that they require o n memory allocations numerical experiences performed on a set of standard benchmarks of mlp networks show the competitivity of the lqn methods especially for large values of n

a numerical verification method for the existence of weak solutions for nonlinear boundary value problems abstract in this paper we consider a numerical technique which enables us to verify the existence of solutions for nonlinear two point boundary value problems bvp we formulate the problem as a fixed point of a newton like operator and present a verification algorithm by computer based on sadovskii s fixed point theorem in order to compute the newton type iterative sequences in infinite dimensional space two concepts the rounding and the rounding error are introduced also some numerical examples are illustrated we emphasize that since the present method uses the weak formulation of bvp and the finite element approximations instead of the existing validation techniques it is aslo applicable in principle to the bvp for partial differential equations as it stands

comments on fast computation of the discrete cosine transform and the discrete hartley transform by h s malvar the commenter shows that the algorithm presented in the above paper ibid vol assp 35 no 10 p 1484 5 oct 1987 requires exactly the same number of multiplications as but more additions than prevalent methods for the computation of the dht discrete hartley transform by existing methods contrary to the author s claim

split vector radix fast fourier transform the split radix approach for computing the discrete fourier transform dft is extended for the vector radix fast fourier transform fft to two and higher dimensions it is obtained by further splitting the n 2 n 2 transforms with twiddle factors in the radix 2 2 fft algorithm the generalization of this split vector radix fft algorithm to higher radices and higher dimensions is also presented by introducing a general approach for constructing the fast hartley transform fht from the corresponding fft new vector and split vector radix fht algorithms with the same desirable properties as their fft counterparts are obtained

fast hartley transforms for image processing the fast hartley transform fht is used to transform two dimensional image data because the hartley transform is real valued it does not require complex operations both spectra and autocorrelations of two dimensional ultrasound images of normal and abnormal livers were computed

numerical verification of solutions for variational inequalities of the second kind abstract the purpose of this paper is to present an approach to the numerical proof of existence of solutions for the problem of the flow of a viscous plastic fluid in a pipe using the finite element approximations and the explicit a priori error estimates for the problem of the flow of a viscous plastic fluid in a pipe we present an effective verification procedure that through numerical computation generates a set which includes the exact solution further a numerical example is presented

a note on 2 d hartley transform in recent years the application of the hartley transform originally introduced by hartley 1942 has gained importance in seismic signal processing and interpretation saatcilar et al 1990 1992 the hartley transform is similar to the fourier transform but is computationally much faster than even the fast fourier transform bracewell 1983 bracewell et al 1986 sorensen et al 1985 pei and wu 1985 duhamel and vetterli 1987 zhou 1992 surprisingly we have not seen a clear definition of the 2 d hartley transform in the published literature