a counterexample to the isomorphism problem for integral group rings let x be a finite group and denote its integral group ring by zx a group basis of zx is a subgroup y of the group of units of zx of augmentation 1 such that zx zy and ixi yi an example of a finite group x is given such that zx has a group basis which is not isomorphic to x a main ingredient is the existence of a subgroup g of x which possesses a non inner automorphism which becomes inner in the integral group ring zg the question whether a finite group x is determined by its integral group ring zx is known as the isomorphism problem for integral group rings it was

simple classical groups of lie type are determined by their character degrees let g be a finite group denote by irr g the set of all irreducible complex characters of g let cd g be the set of all irreducible complex character degrees of g forgetting multiplicities that is cd g 1 irr g and let x1 g be the set of all irreducible complex character degrees of g counting multiplicities let h be a finite nonabelian simple classical group in this paper we will show that if g is a finite group and x1 g x1 h then g is isomorphic to h in particular this implies that the nonabelian simple classical groups of lie type are uniquely determined by the structure of their complex group algebras

on the moore penrose generalized inverse matrix in this paper we exhibit some different methods for computing the moore penrose inverse of different type of matrices we discuss the moore penrose inverse of block matrices full rank factorization we give some numerical computations relative to this theory

relatively robust representations of symmetric tridiagonals let ldlt be the triangular factorization of an unreduced symmetric tridiagonal matrix t i small relative changes in the nontrivial entries of l and d may be represented by diagonal scaling matrices 1 and 2 ldlt 2l 1d 1lt 2 the effect of 2 on the eigenvalues i is benign in this paper we study the inner perturbations induced by 1 suitable condition numbers govern the relative changes in the eigenvalues i we show that when j is an eigenvalue then the relative condition number of m j m j is the same for all n twisted factorizations one of which is ldlt that could be used to represent t i see section 2 we prove that as j the smallest eigenvalue has relative condition number relcond 1 o j each relcond is a rational function of we identify the poles and then use orthogonal polynomial theory to develop upper bounds on the sum of the relconds of all the eigenvalues these bounds require o n operations for an n n matrix we show that the sum of all the relconds is bounded by trace l d lt and conjecture that n ldlt the quantity trace l d lt ldlt is a natural measure of element growth in the context of this paper an algorithm for computing numerically orthogonal eigenvectors without recourse to the gram schmidt process is sketched it requires that there exist values of close to each cluster of close eigenvalues such that all the relconds belonging to the cluster are modest say 10 the sensitivity of the other eigenvalues is not important for this reason we develop o n bounds on the sum of the relconds associated with a cluster none of our bounds makes reference to the nature of the distribution of the eigenvalues within a cluster which can be very complicated

on signed incomplete cholesky factorization preconditioners for saddle point systems limited memory incomplete cholesky factorizations can provide robust preconditioners for sparse symmetric positive definite linear systems in this paper the focus is on extending the approach to sparse symmetric indefinite systems in saddle point form a limited memory signed incomplete cholesky factorization of the form ldl t is proposed where the diagonal matrix d has entries pm 1 the main advantage of this approach is its simplicity as it avoids the use of numerical pivoting instead a global shift strategy involving two shifts one for the 1 1 block and one for the 2 2 block of the saddle point matrix is used to prevent breakdown and to improve performance the matrix is optionally prescaled and preordered using a standard sparse matrix ordering scheme that is then postprocessed to give a constrained ordering that reduces the likelihood of breakdown and need for shifts the use of intermediate memory memory used in the construction of the incomplete factorization but subsequently d

an implicit jacobi like method for computing generalized hyperbolic svd abstract in this paper we introduce a joint hyperbolic orthogonal decomposition of two matrices which we call a generalized hyperbolic singular value decomposition or ghsvd this decomposition can be used for finding the eigenvalues and eigenvectors of a symmetric definite pencil x t x y t y where diag 1 we also present an implicit jacobi like method for computing this ghsvd

a weighted least squares method for scattered data fitting in this paper we present a weighted least squares method to fit scattered data with noise existence and uniqueness of a solution are proved and an error bound is derived the numerical experiments illustrate that our weighted least squares method has better performance than the traditional least squares method in case of noisy data

componentwise perturbation analyses for the qr factorization this paper gives componentwise perturbation analyses for q and r in the qr factorization a qr q mathrm t q i r upper triangular for a given real m times n matrix a of rank n such specific analyses are important for example when the columns of a are badly scaled first order perturbation bounds are given for both q and r the analyses more accurately reflect the sensitivity of the problem than previous such results the condition number for r is bounded for a fixed n when the standard column pivoting strategy is used this strategy also tends to improve the condition of q so usually the computed q and r will both have higher accuracy when we use the standard column pivoting strategy practical condition estimators are derived the assumptions on the form of the perturbation delta a are explained and extended weaker rigorous bounds are also given

on principal blocks of p constrained groups a theorem of k w roggenkamp and l l scott shows that for a finite group g with a normal p subgroup containing its own centralizer any two group bases of the integral group ring mathbb z g are conjugate in the units of mathbb z p g though the theorem presents itself in the work of others and appears to be needed there is no published account there seems to be a flaw in the proof because a theorem appearing in the survey k w roggenkamp the isomorphism problem for integral group rings of finite groups progress in mathematics 95 birkhauser basel 1991 pp 193 220 where the main ingredients of a proof are given is false in this paper it is shown how to close this gap at least if one is only interested in the conclusion mentioned above therefore some consequences of the results of a weiss on permutation modules are stated the basic steps of which any proof should consist are discussed in some detail in doing so a complete yet short proof of the theorem is given in the case that g has a normal sylow p subgroup 2000 mathematical subject classification primary 16u60 secondary 20c05

perturbation analysis for block downdating of a cholesky decomposition let the cholesky decomposition of x rm t x be x rm t x r rm t r where r is upper triangular the cholesky block downdating problem is to determine tilde r such that tilde r rm t tilde r r rm t r z rm t z where z is a block of rows from the data matrix x we analyze the sensitivity of this block downdating problem of the cholesky factorization a measure of conditioning for the cholesky block downdating is presented and compared to the single row downdating case

perturbation analysis for the generalized cholesky factorization let k be a symmetric indefinite matrix suppose that k ljl t is the generalized cholesky factorization of k in this paper we present perturbation analysis for the generalized cholesky factorization we obtain the first order bound on the norm of the perturbation in the generalized cholesky factor also we give rigorous perturbation bounds

fast solving of weighted pairing least squares systems this paper presents a generalization of the weighted least squares wls named weighted pairing least squares wpls which uses a rectangular weight matrix and is suitable for data alignment problems two fast solving methods suitable for solving full rank systems as well as rank deficient systems are studied computational experiments clearly show that the best method in terms of speed accuracy and numerical stability is based on a special 1 2 3 inverse whose computation reduces to a very simple generalization of the usual cholesky factorization backward substitution method for solving linear systems

the normalizer of a metabelian group in its integral group ring abstract in this paper we discuss two cases where all c automorphisms are inner therefore the normalizer property holds for those cases our results generalize a result of marciniak and roggenkamp as an application of our theorems we prove that the normalizer property holds for the integral group ring of a split finite metabelian group with a dihedral sylow 2 subgroup our proofs rely heavily on the method of marciniak and roggenkamp

a class of iterative methods for solving saddle point problems we consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points we are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations we present an iterative method involving two levels of iteration similar in some respects to the uzawa algorithm we relate the rates of convergence of the outer and inner iterations proving that under natural hypotheses the outer iteration achieves the rate of convergence of the inner iteration the technique is applied to finite element approximations of the stokes equations

transverse vibrations of elastically connected double string complex system part i free vibrations this paper analyzes the forced transverse vibrations of an elastically connected double string complex continuous system the general solutions of forced vibrations of strings subjected to arbitrarily distributed continuous loads are found by using the method of expansion in a series of the mode shape functions different cases of exciting loadings are analyzed the action of stationary harmonic loads and moving concentrated forces is considered vibrations caused by the harmonic exciting forces are discussed and conditions of resonance and dynamic vibration absorption are formulated thus the string type dynamic absorber can be used to suppress the excessive vibrations of corresponding string systems the dynamic string type damper is a new concept of a continuous dynamic vibration absorber cdva it is shown that a corresponding two degree of freedom discrete system is an analogue of an elastically connected double string complex system theoretical analysis is illustrated by a numerical example

relative perturbation theory for hyperbolic singular value problem we give relative perturbation bounds for singular values and perturbation bounds for singular subspaces of a hyperbolic singular value problem for the pair g j where g is a full rank matrix and j is a diagonal matrix of signs we consider two types of relative perturbations g g b b d and g g d b b depending whether g has full column or full row rank respectively in both cases we also consider relative element wise perturbations of g which typically occur in numerical computations

a bound for the condition of a hyperbolic eigenvector matrix the hyperbolic eigenvector matrix is a matrix x which simultaneously diagonalizes the pair h j where h is hermitian positive definite and j diag 1 such that x hx and x jx j we prove that the spectral condition of x x is bounded byk x mink d hd where the minimum is taken over all non singular matrices d which commute with j this bound is attainable and it can be simply computed similar results hold for other signature matrices j like in the discretized klein gordon equation

sensitivity analysis for the generalized cholesky factorization abstract the explicit expressions of the normwise mixed and componentwise condition numbers and their upper bounds for the generalized cholesky factorization are first obtained then some improved rigorous perturbation bounds with normwise or componentwise perturbation in the given matrix are derived by bringing together the modified matrix vector equation approach with the method of lyapunov majorant function and the banach fixed point theorem theoretical and experimental results show that these new bounds are always tighter than the corresponding ones in the literature

the spectral properties of the hermitian and skew hermitian splitting preconditioner for generalized saddle point problems in this paper we consider the hermitian and skew hermitian splitting hss preconditioner for generalized saddle point problems with nonzero 2 2 blocks the spectral property of the preconditioned matrix is studied in detail under certain conditions all eigenvalues of the preconditioned matrix with the original system being non hermitian will form two tight clusters one is near 0 0 and the other is near 2 0 as the iteration parameter approaches to zero from above so do all eigenvalues of the preconditioned matrix with the original system being hermitian numerical experiments are given to demonstrate the results

floating point perturbations of hermitian matrices abstract we consider the perturbation properties of the eigensolution of hermitian matrices for the matrix entries and the eigenvalues we use the realistic floating point error measure a a recently demmel and veselic considered the same problem for a positive definite matrix h showing that the floating point perturbation theory holds with constants depending on the condition number of the matrix a dhd where aii 1 and d is a diagonal scaling we study the general hermitian case along the same lines thus obtaining new classes of well behaved matrices and matrix pairs our theory is applicable to the already known class of scaled diagonally dominant matrices as well as to matrices given by factors like those in symmetric indefinite decompositions we also obtain norm estimates for the perturbations of the eigenprojections and show that some of our techniques extend to non hermitian matrices however unlike in the positive definite case we are still unable to describe simply the set of all well behaved hermitian matrices

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

units in orders and integral semigroup rings we continue the investigations on the finite conjugacy centre denoted as u the hyper centre and thus also the second centre z2 u of the unit group u of a z order in a finite dimensional q algebra in particular it is shown that u is finitely generated and z2 u u also conditions are obtained for these two groups to be equal or central applications are given to the unit group of the integral semigroup ring zs of a finite semigroup it follows that often u zs has central height two and z2 u zs u zs this extends earlier results on integral group rings by arora and passi bovdi jespers and juriaans and li and parmenter

on the normalizer problem in this paper the normalizer problem of an integral group ring of an arbitrary group g is investigated it is shown that any element of the normalizer 1 gof g in the group of normalized units 1 gis determined by a finite normal subgroup this reduction to finite normal subgroups implies that the normalizer property holds for many classes of infinite groups such as groups without non trivial 2 torsion torsion groups with a normal sylow 2 subgroup and locally nilpotent groups further it is shown that the commutator of 1 gequals g and 1 g g is finitely generated if the torsion subgroup of the finite conjugacy group of g is finite 2002 elsevier science

a note on the perturbation analysis for the generalized cholesky factorization in this note we consider the perturbation analysis for the generalized cholesky factorization further the conditions for the main theorems of the paper w g wang j x zhao perturbation analysis for the generalized cholesky factorization appl math comput 147 2004 601 606 are weakened by using an alternative method moreover some new perturbation bounds are also derived

relative perturbation theory for a class of diagonalizable hermitian matrix pairs abstract veselic and slapnicar gave a general perturbation result for the eigenvalues of the hermitian matrix pair h k where k is positive definite in this paper their result is generalized to a wider class of hermitian matrix pairs especially estimates for the relative perturbation of eigenvalues of definite pairs are also obtained

existence of the hyperbolic singular value decomposition abstract the hyperbolic singular value decomposition is defined on a general n m matrix and an m m signature matrix pair it is employed in finding the eigenstructure of any matrix that is expressed as the difference of two matrix outer products such differences arise in signal processing applications in the context of the covariance differencing the hyperbolic svd applies in problems where the conventional svd cannot be employed the existence of the hyperbolic singular value decomposition is here extended to the most general case where neither the general matrix nor the matrix product is assumed full rank

rounding error analysis of the classical gram schmidt orthogonalization process this paper provides two results on the numerical behavior of the classical gram schmidt algorithm the first result states that provided the normal equations associated with the initial vectors are numerically nonsingular the loss of orthogonality of the vectors computed by the classical gram schmidt algorithm depends quadratically on the condition number of the initial vectors the second result states that provided the initial set of vectors has numerical full rank two iterations of the classical gram schmidt algorithm are enough for ensuring the orthogonality of the computed vectors to be close to the unit roundoff level

diagonal preserving isomorphisms of etale groupoid algebras abstract work of jean renault shows that for topologically principal etale groupoids a diagonal preserving isomorphism of reduced c algebras yields an isomorphism of groupoids several authors have proved analogues of this result for ample groupoid algebras over integral domains under suitable hypotheses in this paper we extend the known results by allowing more general coefficient rings and by weakening the hypotheses on the groupoids our approach has the additional feature that we only need to impose conditions on one of the two groupoids applications are given to leavitt path algebras

hybrid l 1 l 2 minimization with applications to tomography least squares or l2 solutions of seismic inversion and tomography problems tend to be very sensitive to data points with large errors the lp minimization for 1 p 2 gives more robust solutions but usually with higher computational cost iteratively reweighted least squares irls gives efficient approximate solutions to these lp problems we apply irls to a hybrid l2 l2 minimization problem that behaves like an l2 fit for small residuals and like an l1 fit for large residuals the smooth transition from l2 to l1 behavior is controlled by a parameter that we choose using an estimate of the standard deviation of the data error for linear problems of full rank the hybrid objective function has a unique minimum and irls can be proven to converge to it we obtain a robust efficient method for nonlinear problems a version of the gauss newton algorithm can be applied synthetic crosswell tomography examples and a field data vsp tomography example demonstrate the improvement of the hybrid method over le

isomorphisms of p adic group rings a long standing problem first posed by graham higman 15 and later by brauer 4 is the isomorphism problem for integral group rings given finite groups g and h is it true that zg zh implies g 2 h many authors have worked on this question but progress has been difficult 30 perhaps the best positive result was that of whitcomb in 1968 37 who showed that the implication g h holds for g metabelian dade 9 showed there were counterexamples even in the metabelian case if z were replaced by the family of all fields some mathematicians came to believe the problem was a kind of grammatical accident that counterexamples for z were surely there if difficult to find we ourselves began this investigation looking for counterexamples but found that they were indeed very difficult to find much more difficult than we had anticipated slowly we began to believe that at least some exciting positive results were possible in this paper we answer the isomorphism problem for finite p groups over the p adic integers z zcp and in a very strong way in the normalized units augmentation 1 of z pg there is only one con gay czu ss of groups of order g 1 this answers the isomorphism problem in the affirmative for finite p groups g over z or zp and in addition computes the entire picard group 2 of the category of z g modules in terms of automorphisms of g similarly we are able to settle the isomorphism problem for finite nilpotent groups and compute the associated semilocal picard groups we also treat more general coefficient domains namely integral domains s of characteristic 0 in which no rational prime divisor of the group order is invertible for the sg isomorphism problem and treat similar semilocal dedekind domains for the picard group computations the zassenhaus conjecture concerning the rational behavior of group ring automorphisms is verified for the nilpotent case in this general setting cf corollary 3 below over z we announce a positive answer to the isomorphism

perturbation theory for the eigenvalues of factorised symmetric matrices abstract we obtain eigenvalue perturbation results for a factorised hermitian matrix h gjg where j 2 i and g has full row rank and is perturbed into g g where g is small with respect to g this complements the earlier results on the easier case of g with full column rank applied to square factors g our results help to identify the so called quasidefinite matrices as a natural class on which the relative perturbation theory for the eigensolution can be formulated in a way completely analogous to the one already known for positive definite matrices

the normalizer of a group in the unit group of its group ring let g be a group and r a commutative ring one of the main objects investigated in the theory of group rings is the unit group u s u r g of the group ring rg despite many efforts the structure of this group is very poorly understood especially when the group is infinite the aim of this work is to study the normalizer n s n r g of g in u this group acts by conjugation on g and the group of automorphisms of g obtained in this way is denoted by aut g therefore aut g is isomorphic to nrc r r where c s c r g is the center of u since g n the group inn g of inner automorphisms of g is contained in aut g and by out g we r r denote the group aut grinn g f nrgc out interest in the group n is r motivated by the following properties

computing automorphism groups and testing isomorphisms for modular group algebras abstract we describe a new algorithm for computing automorphism groups and checking isomorphism of nilpotent finite dimensional associative algebras over a finite field the algorithm can also be applied to modular group algebras and thus yields a new approach for checking the modular isomorphism problem we report on its application to the groups of order dividing 2 8 and 3 6

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

new preconditioners for saddle point problems we present new preconditioners based on matrix splittings for the saddle point problems the spectral property of one of the preconditioned matrix is studied in detail numerical examples are used to illustrate the efficiency of the new preconditioners

perturbation analysis for block downdating of the generalized cholesky factorization abstract the generalized cholesky factorization is a generalization of the classical cholesky factorization and its block downdating problem means finding the downdated generalized cholesky factorization when a matrix xx t is subtracted from the original matrix where x is full column rank in this paper we consider the perturbation analysis of this problem some first order perturbation bounds are first obtained using the refined matrix equation approach and the matrix vector equation approach these results generalize the corresponding ones for the block downdating problem of the classical cholesky factorization then the rigorous perturbation bounds are also obtained using the combination of the classical and refined matrix equation approaches each of these bounds is composed of a small constant multiple of the first order term of the corresponding first order perturbation bound and an additional second order term

full block j jacobi method for hermitian matrices abstract the paper considers convergence accuracy and efficiency of a block j jacobi method the method is a proper blas 3 generalization of the known method of veselic for computing the hyperbolic singular value decomposition of rectangular matrices at each step the proposed algorithm diagonalizes the block pivot submatrix the convergence is proved for cyclic strategies which are weakly equivalent to the row cyclic strategy the relative accuracy is proved under the standard conditions numerical tests show improved performance with respect to the block oriented generalization of the original method of veselic combined with the hermitian indefinite factorization the proposed method becomes accurate and efficient eigensolver for hermitian indefinite matrices

a perturbation analysis of the problem of downdating a cholesky factorization abstract the rank one modification of a cholesky factorization r t r zz t d t d where r and d are upper triangular matrices and z is a column vector is called the downdating problem there are many articles devoted to this problem due to its broad range of applications and numerical difficulty this paper serves as a first order parametrized perturbation analysis of this problem

a jacobi eigenreduction algorithm for definite matrix pairs we propose a jacobi eigenreduction algorithm for symmetric definite matrix pairsa j of small to medium size real symmetric matrices withj 2 i j diagonal neitherj nora itself need be definite our jacobi reduction works only on one matrix and usesj orthogonal elementary congruences which include both trigonometric and hyperbolic rotations and preserve the symmetry throughout the process for the rotation parameters only the pivotal elements of the current matrix are needed which facilitates parallelization we prove the global convergence of the method the quadratic convergence was observed in all experiments we apply our method in two situations i eigenreducing a single real symmetric matrix and ii eigenreducing an overdamped quadratic matrix pencil in both cases our method is preceded by a symmetric indefinite decomposition and performed in its one sided variant on the thus obtained factors our method outdoes the standard methods like standard jacobi orqr ql in accuracy in spite of the use of hyperbolic transformations which are not orthogonal a theoretical justification of this behaviour is made elsewhere the accuracy advantage of our method can be particularly drastic if the eigenvalues are of different order in addition in working with quadratic pencils our method is shown to either converge or to detect non overdampedness

the generalized cholesky factorization method for saddle point problems over the past 10 years a variety of iterative methods for saddle point problems have been proposed in this paper we present a class of direct methods the so called generalized cholesky factorization method for solving linear systems arising from saddle point problems or discretization of the stokes equations numerical results illustrate the efficiency of new methods given in this paper

new rigorous perturbation bounds for the generalized cholesky factorization some new rigorous perturbation bounds for the generalized cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained where the componentwise perturbation has the form of backward rounding error for the generalized cholesky factorization algorithm these bounds can be much tighter than some existing ones while the conditions for them to hold are simple and moderate

the normalizer property for integral group rings of frobenius groups we prove that the normalizer property holds for the integral group ring of a finite frobenius group g i e that the normalizer of g in the group of units of its integral group ring is nu g g w here denotes the centre of the unit group

componentwise analysis of direct factorization of real symmetric and hermitian matrices abstract we derive componentwise error bound for the factorization h gjg t where h is a real symmetric matrix g has full column rank and j is diagonal with 1 s on the diagonal we also derive a componentwise forward error bound that is we bound the difference between the exact and the computed factor g in the cases where such a bound is possible we extend these results to the hermitian case and to the well known bunch parlett factorization finally we prove bounds for the scaled condition of the matrix g and show that the factorization can have the rank revealing property

on torsion subgroups in integral group rings of finite groups the object of this article are torsion subgroups of the normalized unit group v zg of the integral group ring zg of a finite group g for specific subgroups w we study the gruenberg kegel graph w it is shown that the central elements of an isolated subgroup u of a group basis h of zg are the normalized units of its centralizer ring czg u moreover nv zg u nh u if g has elementary abelian sylow 2 subgroups of order at most 8 each finite 2 subgroup of v zg is rationally conjugate to a subgroup of g finally torsion subgroups of v zg in the case when g is a minimal simple group are considered it follows that if g is a simple group which admits a non trivial partition for each prime p the p rank of a torsion subgroup of v zg is bounded by that one of g

perturbations of the eigenprojections of a factorized hermitian matrix abstract we give the perturbation bounds for the eigenprojections of a hermitian matrix h gjg where g has full column rank and j is nonsingular under the perturbations of the factor g our bounds hold for example when g is given with elementwise relative error our bounds contain relative gaps between the eigenvalues and may thus be much less pessimistic than the standard norm estimates

isomorphisms of integral group rings of infinite groups abstract this paper deals with the isomorphism problem for integral group rings of infinite groups in the first part we answer a question of mazur by giving conditions for the isomorphism problem to be true for integral group rings of groups that are a direct product of a finite group and a finitely generated free abelian group it is also shown that the isomorphism problem for infinite groups is strongly related to the normalizer conjecture next we show that the automorphism conjecture holds for infinite finitely generated abelian groups g if and only if z g has only trivial units in the second part we partially answer a problem of sehgal it is shown that the class of a finitely generated nilpotent group g is determined by its integral group ring provided g has only odd torsion when g has nilpotency class two then the finitely generated restriction is not needed this together with a result of ritter and sehgal settles the isomorphism problem for finitely generated nilpotency class two groups a link is pointed out between this problem and the dimension subgroup problem

symmetric quasidefinite matrices it is stated here that a symmetric matrix k is quasidefinite if it has the form k begin bmatrix e a t a f end bmatrix where e and f are symmetric positive definite matrices although such matrices are indefinite it is shown that any symmetric permutation of a quasidefinite matrix yields a factorization ldl t this result is applied to obtain a new approach for solving the symmetric indefinite systems arising in interior point methods for linear and quadratic programming these systems are typically solved either by reducing to a positive definite system or by performing a bunch parlett factorization of the full indefinite system at every iteration this is an intermediate approach based on reducing to a quasidefinite system this approach entails less fill in than further reducing to a positive definite system but is based on a static ordering and is therefore more efficient than performing bunch parlett factorizations of the original indefinite system