numerical study of juncture flows a computational study of laminar turbu lent and subsonic supersonic horseshoe vortex systems generated by a cylindrical protuberance mounted on a flat plate is presented various vortex structures have been predicted and are discussed for a low subsonic laminar flow the number of computed vortex arrays increases with reynolds number with fixed incoming boundary layer thickness in agreement with experimental and previous numerical observations the relationships among pressure extrema vorticity and the singular points in the flow structure on the plane of symmetry over the flat plate are studied mach number effects have also been investigated for laminar flow at one reynolds number the outermost singular point moves upstream when freestream mach number increases the size of the whole vortex structure increases dramatically due to shock wave boundary layer interaction the computed laminar horseshoe vortex systems start from a saddle point of attachment in the case of a supersonic turbulent flow at a high reynolds number the computed results predict the same features as those indicated by the experimental results such as the upstream shock wave boundary layer interaction and the classical horseshoe vortex system starting from a saddle point of separation the calculations provide details of the downstream wake shock wave interaction and the near wake tornadolike vortex structure the overall flow topology is discussed

numerical simulation of turbulent cylinder juncture flowfields steady high reynolds number subsonic and supersonic flowfields about a circular cylinder mounted upright on a flat plate were simulated numerically by integration of the time dependent three dimensional compressible mass averaged navier stokes equations effects of turbulence were represented by a two equation k e closure model that included a generalized formulation and low reynolds number terms for the supersonic case the turbulence equations incorporated a compressibility correction grid mesh step size studies were performed to assess resolution requirements of the solutions comparison is made with experimental data in terms of static pressure and total pressure loss coefficients velocity distributions and surface limiting streamline patterns

an iterative substructuring algorithm for equilibrium equations the topic of iterative substructuring methods and more generally domain decomposition methods has been extensively studied over the past few years and the topic is well advanced with respect to first and second order elliptic problems however relatively little work has been done on more general constrained least squares problems or equivalent formulations involving equilibrium equations such as those arising for example in realistic structural analysis applications the potential is good for effective use of iterative algorithms on these problems but such methods are still far from being competitive with direct methods in industrial codes the purpose of this paper is to investigate an order reducing preconditioned conjugate gradient method proposed by barlow nichols and plemmons for solving problems of this type the relationships between this method and nullspace methods such as the force method for structures and the dual variable method for fluids are examined convergence properties are discussed in relation to recent optimality results for varga s theory ofp cyclic sor we suggest a mixed approach for solving equilibrium equations consisting of both direct reduction in the substructures and the conjugate gradient iterative algorithm to complete the computations

block gauss elimination followed by a classical iterative method for the solution of linear systems in the last two decades many papers have appeared in which the application of an iterative method for the solution of a linear system is preceded by a step of the gauss elimination process in the hope that this will increase the rates of convergence of the iterative method this combination of methods has been proven successful especially when the matrix a of the system is an m matrix the purpose of this paper is to extend the idea of one to more gauss elimination steps consider other classes of matrices a e g p cyclic consistently ordered and generalize and improve the asymptotic convergence rates of some of the methods known so far

zero sets of bivariate hermite polynomials abstract we establish various properties for the zero sets of three families of bivariate hermite polynomials special emphasis is given to those bivariate orthogonal polynomials introduced by hermite by means of a rodrigues type formula related to a general positive definite quadratic form for this family we prove that the zero set of the polynomial of total degree n m consists of exactly n m disjoint branches and possesses n m asymptotes a natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property the results show that the properties of the zero sets considered as affine algebraic curves in r 2 are completely different for the three families analyzed

extrapolated gauss seidel i and sor methods for least squares problems recently special attention has been given in the literature to the problems of accurately computing the least squares solution of very largescale over determined systems of linear equations which occur in geodetic applications in particular it has been suggested that one can solve such problems iteratively by applying the block sor successive overrelaxation and egs1 extrapolated gauss seidel 1 plus semi iterative methods to a linear system with coefficient matrix 2 cyclic or 3 cyclic the comparison of 2 block sor and 3 block sor was made in 1 and showed that the 2 block sor is better in 6 the authors also proved that 3 block egs1 si is better than 3 block sor here we first show that the 2 block dj double jacobi si gs si and egs1 si methods are equivalent and all of them are equivalent to the 3 block egs1 si method then we prove that the composite methods and 2 block sor have the same asymptotic rate of convergence but the former has a better average rate of convergence finally numerical experiments are reported and confirm that the 3 block egs1 si is better than the 2 block sor

a young eidson s type algorithm for complex p cyclic sor spectra abstract in a recent work of ours we have solved the problem of the minimization of the spectral radius of the iteration matrix of a p cyclic successive overrelaxation sor method for the solution of the linear system ax b when the matrix a is block p cyclic consistently ordered for what is known as the one point problem for any p 3 particular cases of the one point problem were solved by young varga kjellberg kredell russell and others in the present work we develop a theory using the results of our previous one and solve first the two point problem special cases of which were solved by wrigley eiermann niethammer ruttan noutsos and others secondly we generalize and extend our theory to cover the many point problem and develop a young eidson s type algorithm for its solution as possible application areas we mention among others the best block p cyclic repartitioning for the sor method are the solution of large scale systems arising in queueing network problems in markov analysis

experimental study of saddle point of attachment in laminar juncture flow an experimental study of laminar horseshoe vortex flows upstream of a cylinder flat plate juncture has been conducted to verify the existence of saddle point of attachment topologies in the classical depiction of this flowfield a saddle point of separation exists on the flat plate upstream of the cylinder and the boundary layer separates from the surface recent computations have indicated that the topology may actually involve a saddle point of attachment on the surface and additional singular points in the flow laser light sheet flow visualizations have been performed on the symmetry plane and crossflow planes to identify the saddle point of attachment flowfields the visualizations reveal that saddle point of attachment topologies occur over a range of reynolds number in both single and multiple vortex regimes an analysis of the flow topologies is presented that describes the existence and evolution of the singular points in the flowfield

the numerical solution of equality constrained quadratic programming problems this paper proves that a large class of iterative schemes can be used to solve a certain constrained minimization problem the constrained minimization problem considered involves the minimization of a quadratic functional subject to linear equality constraints among this class of convergent iterative schemes are generalizations of the relaxed jacobi gauss seidel and symmetric gauss seidel schemes

accuracy of preconditioned cg type methods for least squares problems abstract the conjugate gradient method with imgs an incomplete modified version of gram schmidt orthogonalization to obtain an incomplete orthogonal factorization preconditioner applied to the normal equations pcgls is often used as the basic iterative method to solve the linear least squares problems in this paper a detailed analysis is given for understanding the effect of rounding errors on imgs and determining the accuracy of computed solutions of pcgls with imgs for linear least squares problems in finite precision it is shown that for a consistent system the difference between the true residuals and the updated approximate residual vectors generated depends on the machine precision e on the maximum growth in norm of the iterates over their initial values the norm of the true solution and the condition number of r which is affected by the drop set in incomplete gram schmidt factorization similar results are obtained for the difference between the true and computed solution for inconsistent systems numerical tests are carried out to confirm the theoretical conclusions

a survey of the iterative methods for the solution of linear systems by extrapolation relaxation and other techniques abstract for the iterative solution of linear systems of algebraic equations ax b 1 with a c n n x b c n and det a 0 numerous methods exist although a classification of them seems not to be possible one may note that the first step for the construction of an iterative method usually begins with a splitting of a in 1 thus a is written as a m n where det m 0 and m is easily inverted so that 1 is equivalent to x tx c 2 t m 1n c m 1 the discussion will be restricted to the so called linear stationary iterative methods although some nonstationary ones will be mentioned and emphasis will be given to those which fall into the categories of extrapolation relaxation and similar ones for this it will be assumed that the spectrum t of t in 2 is contained in a well defined compact region r whose complement with respect to the complex plane is simply connected and 1 r under these assumptions and for each specific class of methods described each time an attempt will be made to present the optimum one the optimum is the one out of the class of methods for which the sequence of vectors yielded converges asymptotically to the unique solution of 1 as fast as possible

an algorithmic approach for the analysis of extrapolated iterative schemes applied to least squares problems abstract the problem of determining the optimal values of extrapolated iterative schemes as they apply to the solution of large scale least squares problems is addressed here based on algebraic and geometric eigenvalue properties of the accelerated gauss seidel ags we devise a simple algorithmic procedure which successfully yields the optimal values of the extrapolated ags eags comparisons with the optimal sor scheme reveal that the two optimal schemes strongly compete numerical examples are used to demonstrate our results

order reducing conjugate gradients versus block aor for constrained least squares problems abstract we compare the convergence properties of two iterative algorithms for solving equality constrained least squares problems the first algorithm due to barlow nichols and plemmons applies a variation of the conjugate gradient algorithm to a symmetric positive definite system which is smaller than the original problem the second block accelerated overrelaxation is a two parameter generalization of block sor barlow nichols and plemmons have proven that their order reducing conjugate gradient algorithm converges faster than block sor we extend their result to show that the algorithm is also superior to block aor numerical experiments on some structural engineering problems support the analysis

minimization of l 2 norms of the sor and msor operators the average behavior of the sor method and the msor method is studied for matrices whose jacobian matrix is skew symmetric matrix the objective is to find the values of optimal parameters to minimize the l 2 norm of the sor and msor operators based on the eigenvalue functional given by yin and yuan appl math comput 127 2002 327 333

on computational procedures for the force method it is known that the matrix force method has certain advantages over the displacement method for a class of structural problems it is also known that the force method when carried out by the conventional gauss jordan procedure tends to fill in the problem data making the method unattractive for large size sparse problems this poor fill in property however is not necessarily inherent to the method and the sparsity may be maintained if one uses what we call the turn back lu procedure the purpose of this paper is two fold first it is shown that there exist some close relationships between the force method and the least squares problem and that many existing algebraic procedures to perform the force method can be regarded as applications extensions of certain well known matrix factorization schemes for the least squares problem secondly it is demonstrated that these algebraic procedures for the force method can be unified form the matrix factorization viewpoint included in this unification is the turn back lu procedure which was originally proposed by topcu in his thesis 8 it is explained why this procedure tends to produce sparse and banded self stress and flexibility matrices with small band width some computational results are presented to demonstrate the superiority of the turn back lu procedure over the other schemes considered in this paper

computation of saddle point of attachment because of is reputed benign nature the saddle point of attachment has not received critical attention to nearly the same extent as has the saddle point of separation recently visbal calculated low speed flows around a cylinder mounted on a flat plate here it was fully to be expected that the outermost critical point in the surface flow pattern ahead of the obstacle would be a saddle point of separation the results indicated that the critical point was actually a saddle point of attachment not separation

computation of navier stokes equations for three dimensional flow separation supersonic flows over a sharp and a flat faced blunt fin mounted on a flat plate are simulated numerically several basic issues involved in the resultant three dimensional steady flow separation are studied using the same number of grid points different grid spacings are employed to investigate the effects of a grid resolution on the origin of the line of separation various shock strengths are used to study the so called separation and unseparated boundary layer and to establish the existence or absence of secondary separation the length of separation ahead of the flat faced blunt fin bifurcation of a horseshoe vortex and the accessibility of a closed type separation are investigated the usual interpretation of the flow field from previous studies and new interpretations arising from the present simulation are discussed

optimal successive overrelaxation iterative methods for p cyclic matrices we consider linear systems whose associated block jacobi matricesj p are weakly cyclic of indexp in a recent paper pierce hadjidimos and plemmons 13 proved that the block two cyclic successive overrelaxation sor iterative method is numerically more effective than the blockq cyclic sor method 2 2 finally as a counterpart to the result of pierce hadjidimos and plemmons we show that under this more general assumption the two cyclic sor method is not always superior to theq cyclic sor method 2 q p

multivariate stieltjes type theorems and location of common zeros of multivariate orthogonal polynomials invariant factors of bivariate orthogonal polynomials inherit most of the properties of univariate orthogonal polynomials and play an important role in the research of stieltjes type theorems and location of common zeros of bivariate orthogonal polynomials the aim of this paper is to extend our study of invariant factors from two variables to several variables we obtain a multivariate stieltjes type theorem and the relationships among invariant factors multivariate orthogonal polynomials and the corresponding jacobi matrix we also study the location of common zeros of multivariate orthogonal polynomials and provide some examples of tri variate

implicit multiple grid solution of the compressible navier stokes equations using k epsilon turbulence closure in the present work an algorithm for the numerical solution of the two dimensional mass weighted ensemble averaged compressible navier stokes equations is presented turbulence closure for the reynolds stresses is obtained using a low reynolds n umber two equation k s model which includes near wall effects the same algorithm is used for the integration of both the navier stokes and the turbulence transport equations the algorithm consists of a basic explicit finite volume scheme whose convergence is accelerated using local time step ping and multiple grid techniques convergence is further enhanced by the use of an implicit residual smoothing technique applied both in the fine and the coarser grids the application of the numerical scheme to the solution of the k s equations is examined in detail comparisons of computations with experimental data are presented for three shock wave turbulent boundary layer interaction flows algorithm convergence rate and cpu time require ments are discussed he numerical solution of the navier stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work 1 interest is focused both on code applicability to variegated config urations and on computational rapidity although direct simulation of turbulent flows2 or large eddy numerical sim ulations using subgrid turbulence modeling 3 4 have appeared in the literature current status of algorithm development and computer power indicate that for practical applications the ensemble averaged navier stokes equations should be used in conjunction with transport equations for turbulence closure 5 7 algebraic or mixing length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear layer thickness and of the distance of each grid point from the solid boundary thus they lack both geometric invariance and locality which are highly desirable properties from a computational viewpoint when addressing complex flowfields with many interacting solid boundaries although research on reynolds stre ss transport closure appears quite promising 9 10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved also further research con cerning wall effects is required the more so since the use of wall functions is considered inadequate 11 on the other hand the use of two equation closures such as a 12 14 is quite widespread notwithstanding the fact that the use of the boussinesq hypothesis15 introduces a question able simplification of the flow physics 16 the major drawback of the k s model is probably the near wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence several variants of the original jones launder model12 have been developed in an attempt to improve upon near wall modeling some ten such models have been thor oughly examined in a critical review article by patel et al 17 who concluded that the models of launder and sharma 14

optimal p cyclic sor for complex spectra abstract we consider the successive overrelaxation sor method for the solution of a linear system ax b when the matrix a has a block p p partitioned p cyclic form and its associated block jacobi matrix jp is weakly cyclic of index p following the pioneering work by young and varga in the 1950s many researchers have considered various cases for the spectrum jp and have determined optimal values for the relaxation factor 0 2 so that the sor method converges as fast as possible after the most recent work on the best block p cyclic repartitioning and that on the solution of large scale systems arising in queueing network problems in markov analysis the optimization of the convergence of the p cyclic sor for more complex spectra jp has become more demanding here we state the one point problem for the general p cyclic complex sor case the existence and the uniqueness of its solution are established by analyzing and developing further the theory of the associated hypocycloidal curves for the determination of the optimal parameter s an algorithm is presented and a number of illustrative numerical examples are given

evaluation of explicit algebraic reynolds stress models for separated supersonic flows high reynolds number supersonic e owe elds were generated numerically to assess the performance of three explicit algebraic reynolds stress turbulence models the cone gurations consist of a shock boundary layer interaction and a 24 deg compression ramp both of which exhibit an appreciable region of separated e ow solutions were also obtained using standard zero equation and k models details of the computations are summarized and the accuracy of numerical results is established via grid resolution studies comparisons are made with experimental data in terms of surface pressure and skin friction as well as off surface proe les of mean velocity and componentsofthereynolds stresstensor forthee owsconsidered here it isfound that thealgebraic stressmodels offer little improvement over existing closures

thin layer full navier stokes simulations over a supersonic delta wing steady flowfields describing the flow over a 75 deg swept delta wing at m 1 95 and re 4 48 10 6 were simulated at 20 and 30 deg using two computer codes comparisons were made between calculations using 1 the laminar and turbulent thin layer navier stokes equations and 2 laminar thin layer and navier stokes equations

numerical methods for generalized least squares problems usually generalized least squares problems are solved by transforming them into regular least squares problems which can then be solved by well known numerical methods however this approach is not very effective in some cases and besides is very expensive for large scale problems in 1979 paige suggested another approach which consists of solving an equivalent equality constrained least squares problem by the orthogonal decomposition the bnp algorithm or the james implicit nullspace iterative methods in this paper we present some new developments of the numerical methods for example 2 cycle sor method and preconditioned conjugate gradient method for generalized least squares problems some numerical comparisons are included as well

stieltjes type theorems for orthogonal polynomials of two variables in this paper some important properties of orthogonal polynomials of two variables are investigated the concepts of invariant factor for orthogonal polynomials of two variables are introduced the presented results include stieltjies type theorems for multivariate orthogonal polynomials and the corresponding asymptotic expansion formulas

the analysis ofk step iterative methods for linear systems from summability theory using the theory of euler methods from summability theory we investigate general iterative methods for solving linear systems of equations in particular for a given euler method a regions of the complex plane is determined such that ak step iterative method converges if the eigenvalues of an iteration operatort are contained ins for a givens optimal methods are described and upper and lower bounds are derived for the associated asymptotic rate of convergence special attention is given to two step methods with complex parameters

structure of a turbulent double fin interaction at mach 4 this paper examines the three dimensional shock wave turbulent boundary layer interaction in an inletlike geometry consisting of symmetrically placed 15 deg fins on a plate in an oncoming mach 4 flow two different implicit numerical methods are employed to solve the full three dimensional mean compressible navier stokes equations 1 a high resolution upwind scheme with the baldwin lomax algebraic turbulence model and 2 the traditional beam warming approach with a k e model the comparison with experiment is very good for surface pressures pitot pressure surveys and surface shear patterns although discrepancies with skin friction data are evident in the trailing portion of the interaction both computational schemes despite major differences in modeling predict similar flow structures in agreement with previous results at mach 8 the flow is described in terms of a separated nonreattaching boundary layer a vortex interaction longitudinal centerline vortices and entrainment the computed and experimental shock patterns are related to the streamline structure to provide a unified understanding of the flowfield

a result on common zeros location of orthogonal polynomials in two variables abstract the aim of this paper is to investigate some general properties of common zeros of orthogonal polynomials in two variables for any given region d r 2 from a view point of invariant factor an important result is shown that if x 0 is a common zero of all the orthogonal polynomials of degree k then the intersection of any line passing through x 0 and d is not empty this result can be used to settle the problem of location of common zeros of orthogonal polynomials in two variables the main result of the paper can be considered as an extension of the univariate case

structure of laminar juncture flows a computational study of both steady and periodic laminar horseshoe vortex flows generated upstream of a cylinder flat plate juncture is presented the flowfields are simulated using the full three dimensional unsteady navier stokes equations and a time accurate implicit algorithm a new type of laminar horseshoe vortex topology is identified for the case of a single primary vortex this new topology is found to be independent of the computational grid and is also supported by recent experimental flow visualizations the flat plate skin friction portraits corresponding to the new and to the standard horseshoe vortex topologies are equivalent pointing out the nonunique relation between the wall limiting streamline pattern and the three dimensional flow above the plate for the new topology the foremost line of coalescense is an attachment rather than a separation line this unusual feature illustrates the fact that convergence of skin friction lines is a necessary but not sufficient condition for separation as the reynolds number increases the flow topology evolves from a single to multiple primary horseshoe vortices in agreement with experimental observations at least two different types of triple horseshoe vortex systems are shown to be possible above a certain value of the reynolds number the juncture flow becomes unsteady and periodic at a frequency that increases with reynolds number the unsteady horseshoe vortex process upstream of the cylinder is found in qualitative agreement with experiment horseshoe vortices are periodically generated and convected toward the juncture vorticity intensification by vortex stretching and the eruption of vorticity from the plate surface are observed

numerical analysis of three dimensional viscous internal flows a 3 d navier stokes code has been developed for analysis of turbomachinery blade rows and other internal flows the navier stokes equations are written in a cartesian coordinate system rotating about the x axis and then mapped to a general body fitted coordinate system streamwise viscous terms are neglected using the thin layer assumption and turbulence effects are modeled using the baldwin lomax turbulence model the equations are discretized using finite differences on stacked c type grids and are solved using a multistage runge kutta algorithm with a spatially varying time step and implicit residual smoothing calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer comparisons are made with experimental data taken by eckerle and langston for a circular cylinder under similar conditions computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane calculated details of the primary vortex show excellent agreement with the experimental data the calculations also show a small secondary vortex not seen experimentally

convergence of a direct iterative method for large scale least squares problems abstract in 1975 chen and gentleman suggested a 3 block sor method for solving least squares problems based on a partitioning scheme for the observation matrix a into a a 1 a 2 where a1 is square and nonsingular in many cases a1 is obvious from the nature of the problem this combined direct iterative method was discussed further and applied to angle adjustment problems in geodesy where a1 is easily formed and is large and sparse by plemmons in 1979 recently niethammer de pillis and varga have rekindled interest in this method by correcting and extending the sor convergence interval the purpose of our paper is to discuss an alternative formulation of the problem leading to a 2 block sor method for this formulation it is shown that the resulting direct iterative method always converges for sufficiently small sor parameter in contrast to the 3 block formulation formulas for the optimum sor parameter and the resulting asymptotic convergence factor based upon a2a 11 2 are given furthermore it is shown that this 2 cyclic block sor method always gives better convergence results than the 3 cyclic one for the same amount of work per iteration the direct part of the algorithm requires only a sparse matrix factorization of a1 our purpose here is to establish theoretical convergence results in line with the purpose of the recent paper by niethammer de pillis and varga practical considerations of choosing a1 in certain applications and of estimating the resulting a2a 11 2 will be addressed elsewhere

a note on two block sor methods for sparse least squares problems abstract we compare two recently proposed block sor methods for the solution of large least squares problems with the conjugate gradient algorithm for solving the specially preconditioned normal equations by proving that all three methods are based on the same krylov sequence we show that the conjugate gradient algorithm is generally preferable to the two sor approaches

successive overrelaxation methods for solving the rank deficient linear squares problem abstract we develop successive overrelaxation sor methods for finding the least squares solution of minimal norm to the system ax b where a is an m n matrix of rank r the methods are obtained by first augmenting the system to a block 4 4 consistent system of linear equations the augmented coefficient matrix is then split by a subproper sor splitting an interval for the relaxation parameter in which the subproper sor iteration matrix is semiconvergent is determined along with the optimal relaxation parameter which minimizes the modulus of the controlling eigenvalue of the sor matrix since the scheme computes at first only a solution to the augmented system it is subsequently shown how to transform such a solution to the unique solution of minimal 2 norm analysis of the practical implementation of the algorithms developed here will be given elsewhere

a parallelizable sor like method systems with plus shaped and linear spectra abstract the classical sor method replaces an invertible cyclic linear system in b x f with a family of systems i n b x f where for some optimal scalar b the spectrum of b b is circular the eigenvalues of b are linearly placed falling on the real line moreover the spectral radius of b b is less than that of b similarly this paper explores a tensor mechanism which converts more general systems in b x f to equivalent systems i 2n b x f where the spectrum of b may be plus shaped the spectrum of b is circular and x col 0 x as in the sor theory the spectral radius of b is less than that of b among other things we recapture the results of the sor theory improve on some known results and extend our theory directly to matrices in b which need not be symmetric yet have real plus and minus valued eigenvalues

superior convergence domains for the p cyclic ssor majorizer abstract thus far for an n n complex nonsingular matrix a the symmetric successive overrelaxation ssor majorizing operator has been used to establish convergence properties of the ssor method mostly in the case where a is an h matrix in this paper we use actually a similarity transformation of the ssor majorizer to investigate convergence properties of the block ssor method when a is a block p cyclic matrix let ja denote the block jacobi method and let j a we establish regions in the plane where s a q a l a here s a is the block ssor iteration operator associated with a l a is the block successive overrelaxation sor iteration operator associated with a and q a is a convenient similarity transformation of the majorizing operator for s a of special interest to us are the values of for which the above inequality holds for the corresponding values of the relaxation parameter a 2 1 the latter being an important quantity in the sor ssor theory for h matrices

preconditioned iterative methods for solving linear least squares problems new preconditioning strategies for solving m times n overdetermined large and sparse linear least squares problems using the conjugate gradient for least squares cgls method are described first direct preconditioning of the normal equations by the balanced incomplete factorization bif for symmetric and positive definite matrices is studied and a new breakdown free strategy is proposed preconditioning based on the incomplete lu factors of an n times n submatrix of the system matrix is our second approach a new way to find this submatrix based on a specific weighted transversal problem is proposed numerical experiments demonstrate different algebraic and implementational features of the new approaches and put them into the context of current progress in preconditioning of cgls it is shown in particular that the robustness demonstrated earlier by the bif preconditioning strategy transfers into the linear least squares solvers and the use of the weighted transversal helps to improve the lu

block sor methods for rank deficient least squares problems many papers have discussed preconditioned block iterative methods for solving full rank least squares problems however very few papers studied iterative methods for solving rank deficient least squares problems miller and neumann 1987 proposed the 4 block sor method for solving the rank deficient problem here a 2 block sor method and a 3 block sor method are proposed to solve such problem the convergence of the block sor methods is studied the optimal parameters are determined comparison between the 2 block sor method and the 3 block sor method is given also

convergence of block iterative methods applied to sparse least squares problems abstract recently special attention has been given in the mathematical literature to the problems of accurately computing the least squares solutions of very large scale overdetermined systems of linear equations such as those arising in geodetical network problems in particular it has been suggested that one solve such problems iteratively by applying the block sor successive overrelaxation iterative method to a consistently ordered block jacobi matrix that is weakly cyclic of index 3 here we obtain new results theorem 1 giving the exact convergence and divergence domains for such iterative applications it is then shown how these results extend and correct the literature on such applications in addition analogous results theorem 2 are given for the case when the eigenvalues of the associated block jacobi matrix are nonnegative

a note on the sor and cg methods for large least squares problems abstract the sor and cg methods are considered for least squares problems the sor and cg methods are preferable with respect to storage and multiplication requirements to the 2 block sor given in 1 and the cg algorithm in 2 when the problem is of large scale

numerical investigation of supersonic wing tip vortices steady high reynolds number flowfields about a finite span rectangular wing mounted upright in a supersonic stream were generated numerically to investigate formation of the tip vortex solutions were obtained by integration of the time dependent three dimensional compressible euler and thin layer laminar and mass averaged turbulent navier stokes equations in the turbulent case a two equation k e closure model was employed which included low reynolds number terms and a compressibility correction details of the computations are summarized and a grid resolution study is provided to assess the accuracy of the numerical results comparisons are made between solutions of the various governing equations as well as with experimental data in terms of pressure and mach number component distributions in the vortex core

preconditioned conjugate gradient method for generalized least squares problems abstract a variant of the preconditioned conjugate gradient method to solve generalized least squares problems is presented if the problem is min ax b t w 1 ax b with a r m n and w r m m symmetric and positive definite the method needs only a preconditioner a 1 r n n but not the inverse of matrix w or of any of its submatrices freund s comparison result for regular least squares problems is extended to generalized least squares problems an error bound is also given

convergence domains of the ssor method for a class of generalized consistently ordered matrices abstract the functional equation relating the eigenvalues of the block symmetric successive overrelaxation ssor iteration matrix with those of the block jacobi iteration matrix found by chong and cai 1985 is used in order to obtain precise domains of convergence of the block ssor iteration method associated with a class of generalized consistently ordered gco k p k matrices a p 2 k 1 p 1 we show that the domain of convergence depends only on the relaxation parameter the spectral radius of the block jacobi iteration matrix and the value of l k p unlike the case k p k 1 p 1 p 3 which was studied in an earlier paper by the authors 1989 beyond certain critical values of l the domain of convergence does not grow monotonically with l and manifests various sorts of behavior however as in the case k p k 1 p 1 it is shown that the intersection of the convergence domains taken over all pairs p k coincides with the exact domain of convergence of the point ssor iteration method associated with nonsingular h matrices a that is matrices which can be diagonally scaled to being strictly diagonally dominant

a time split finite volume algorithm for three dimensional flowfield simulation a general finite volume algorithm is developed for solving three dimensional time dependent compressible navier stokes equations for high reynolds number flows over an arbitrary geometry this algorithm adapts maccormack s 1982 explicit implicit scheme to a time split three dimensional finite volume concept in a general coordinate system it is shown that the thin layer approximation in all three spatial directions significantly reduces the evaluation of viscous terms and allows the algorithm to solve more complicated geometries with all boundaries in two or all three directions the calculated results using this method are found to be in good agreement with the experimental measurements of a blunt fin induced shock wave and boundary layer interaction problems observations of the existence of peak pressure primary horseshoe and secondary vortices and reversed supersonic zones show that computational fluid dynamics can effectively supplement the wind tunnel tests for aerodynamic design as well as for understanding basic fluid dynamics

successive overrelaxation sor and related methods abstract covering the last half of the 20th century we present some of the basic and well known results for the sor theory and related methods as well as some that are not as well known most of the earlier results can be found in the excellent books by varga matrix iterative analysis prentice hall englewood cliffs nj 1962 young iterative solution of large linear systems academic press new york 1971 and berman and plemmons nonnegative matrices in the mathematical sciences siam philadelphia pa 1994 while some of the most recent ones are given in the bibliography of this paper in this survey both the point and the block sor methods are considered for the solution of a linear system of the form ax b where a c n n and b c n 0 some general results concerning the sor and related methods are given and also some more specific ones in cases where a happens to possess some further property e g positive definiteness l m h matrix property p cyclic consistently ordered property etc

block aor iterative schemes for large scale least squares problems the problem of accelerating the convergence rate of iterative schemes as they apply to the solution of large scale least squares problems by means of different splittings is addressed here new convergence results together with explicit expressions for the optimal factors and their corresponding spectral radii are derived for certain schemes from the block accelerated overrelaxation aor family it is shown that for a class of least squares problems the proposed optimal block iterative scheme converges unconditionally and asymptotically faster than the optimal block successive overrelaxation sor method while in all other cases the two schemes are competitive numerical examples are used to illustrate our results

optimal p cyclic sor our purpose in this paper is to extend p cyclic sor theory to consistent singular systems and to apply the results to the solution of large scale systems arising em e g in queueing network problems in markov analysis markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer communication and transportation systems for certain important classes of singular problems we develop a convergence theory for p cyclic sor and show how to repartition for optimal convergence results by kontovasilis plemmons and stewart on the concept of convergence of sor in an em extended sense are rigorously analyzed and applied to the solution of periodic markov chains with period p 2

optimality relationships forp cyclic sor the optimality question for blockp cyclic sor iterations discussed in young and varga is answered under natural conditions on the spectrum of the block jacobi matrix in particular it is shown that repartitioning a blockp cyclic matrix into a blockq cyclic form q p results in asymptotically faster sor convergence for the same amount of work per iteration as a consequence block 2 cyclic sor is optimal under these conditions