首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
Summary Utilizing kernel structure properties a unified construction of Hankel matrix inversion algorithms is presented. Three types of algorithms are obtained: 1)O(n 2) complexity Levinson type, 2)O (n) parallel complexity Schur-type, and 3)O(n log2 n) complexity asymptotically fast ones. All algorithms work without additional assumption (like strong nonsingularity).  相似文献   

2.
In this paper the problem of complexity of multiplication of a matrix with a vector is studied for Toeplitz, Hankel, Vandermonde, and Cauchy matrices and for matrices connected with them (i.e., for transpose, inverse, and transpose to inverse matrices). The proposed algorithms have complexities of at most O(n log2n) flops and in a number of cases they improve the known estimates. In these algorithms, in a separate preprocessing phase, are singled out all the actions on the preparation of a given matrix which aimed at the reduction of the complexity of the second stage of computations directly connected with multiplication by an arbitrary vector. Effective algorithms for computing the Vandermonde determinant and the determination of a Cauchy matrix are given.  相似文献   

3.
4.
Summary It was recently shown that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix. On the other hand, as it is well-known that the inverse of a strictly diagonally dominant Stieltjes matrix is a real symmetric matrix with nonnegative entries, it is natural to ask, conversely, if every strictly diagonally dominant Stieltjes matrix has a strictly ultrametric inverse. Examples show, however, that the converse is not true in general, i.e., there are strictly diagonally dominant Stieltjes matrices in n×n (for everyn3) whose inverses are not strictly ultrametric matrices. Then, the question naturally arises if one can determine which strictly diagonally dominant Stieltjes matrices, in n×n (n3), have inverses which are strictly ultrametric. Here, we develop an algorithm, based on graph theory, which determines if a given strictly diagonally dominant Stieltjes matrixA has a strictly ultrametric inverse, where the algorithm is applied toA and requires no computation of inverse. Moreover, if this given strictly diagonally dominant Stieltjes matrix has a strictly ultrametric inverse, our algorithm uniquely determines this inverse as a special sum of rank-one matrices.Research supported by the National Science FoundationResearch supported by the Deutsche Forschungsgemeinschaft  相似文献   

5.
On neighbouring matrices with quadratic elementary divisors   总被引:1,自引:0,他引:1  
Summary Algorithms are presented which compute theQR factorization of an order-n Toeplitz matrix inO(n 2) operations. The first algorithm computes onlyR explicitly, and the second computes bothQ andR. The algorithms are derived from a well-known procedure for performing the rank-1 update ofQR factors, using the shift-invariance property of the Toeplitz matrix. The algorithms can be used to solve the Toeplitz least-squares problem, and can be modified to solve Toeplitz systems inO(n) space.  相似文献   

6.
Instead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ntr M/(det M)1/n, where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B-reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well-known preconditioned CG methods.  相似文献   

7.
Given n+1 pairs of complex numbers and vectors (closed under complex conjugation), the inverse quadratic eigenvalue problem is to construct real symmetric or anti-symmetric matrix C and real symmetric matrix K of size n×n so that the quadratic pencil Q(λ)=λ2In+λC+K has the given n+1 pairs as eigenpairs. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are obtained. Numerical algorithms for solving the problem are developed. Numerical examples illustrating these solutions are presented.  相似文献   

8.
The local existence and local asymptotic stability of nontrivial p-periodic solutions of p-periodically forced discrete systems are proven using Liapunov-Schmidt methods. The periodic solutions bifurcate transcritically from the trivial solution at the critical value n=ncr of the bifurcation parameter with a typical exchange of stability. If the trivial solution loses (gains) stability as n is increased through ncr , then the periodic solutions on the nontrivial bifurcating branch are locally asymptotically stable if and only if they correspond to n>ncr (n ncr ).  相似文献   

9.
In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a new fast approach to compute the factorization in O(n 2) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness of our approach.  相似文献   

10.
We develop a general framework for perturbation analysis of matrix polynomials. More specifically, we show that the normed linear space Lm(Cn×n) of n-by-n matrix polynomials of degree at most m provides a natural framework for perturbation analysis of matrix polynomials in Lm(Cn×n). We present a family of natural norms on the space Lm(Cn×n) and show that the norms on the spaces Cm+1 and Cn×n play a crucial role in the perturbation analysis of matrix polynomials. We define pseudospectra of matrix polynomials in the general framework of the normed space Lm(Cn×n) and show that the pseudospectra of matrix polynomials well known in the literature follow as special cases. We analyze various properties of pseudospectra in the unified framework of the normed space Lm(Cn×n). We analyze critical points of backward errors of approximate eigenvalues of matrix polynomials and show that each critical point is a multiple eigenvalue of an appropriately perturbed polynomial. We show that common boundary points of components of pseudospectra of matrix polynomials are critical points. As a consequence, we show that a solution of Wilkinson’s problem for matrix polynomials can be read off from the pseudospectra of matrix polynomials.  相似文献   

11.
Given a totally ordered setT containing at leastn+1 elements (say a subset ofR 1), the graph of the functiona:TR n is called a Chebyshev curve (inR n) if the determinant of the matrix (a(t 1),a(t 2), ...,a(t n)) is either positive whenevert 1<t 2<...<t n or negative whenevert 1<t 2<...<t n. For finiteT a characterization of these curves (sequences) has been given by the author.In this paper the result is extended to non-finiteT. The characterization proved here is an improved (reformulated) version of that given by the author for infiniteT.  相似文献   

12.
We present an efficient algorithm for generating an n × n nonsingular matrix uniformly over a finite field. This algorithm is useful for several cryptographic and checking applications. Over GF[2] our algorithm runs in expected time M(n) + O(n2), where M(n) is the time needed to multiply two n × n matrices, and the expected number of random bits it uses is n2 + 3. (Over other finite fields we use n2 + O(1) random field elements on average.) This is more efficient than the standard method for solving this problem, both in terms of expected running time and the expected number of random bits used. The standard method is to generate random n × n matrices until we produce one with nonzero determinant. In contrast, our technique directly produces a random matrix guaranteed to have nonzero determinant. We also introduce efficient algorithms for related problems such as uniformly generating singular matrices or matrices with fixed determinant. © 1993 John Wiley & Sons, Inc.  相似文献   

13.
It is proved that computing the subordinate matrix norm ∥A∥∞1 is NP-hard, Even more, existence of a polynomial-time algorithm for computing this norm with relative accuracy less than 1/(4n2 ), where n is matrix size, implies P = NP.  相似文献   

14.
We study asymptotically fast multiplication algorithms for matrix pairs of arbitrary di- mensions, and optimize the exponents of their arithmetic complexity bounds. For a large class of input matrix pairs, we improve the known exponents. We also show some applications of our results:(i) we decrease from O(n~2 n~(1 o)(1)logq)to O(n~(1.9998) n~(1 o(1))logq)the known arithmetic complexity bound for the univariate polynomial factorization of degree n over a finite field with q elements; (ii) we decrease from 2.837 to 2.7945 the known exponent of the work and arithmetic processor bounds for fast deterministic(NC)parallel evaluation of the determinant, the characteristic polynomial, and the inverse of an n×n matrix, as well as for the solution to a nonsingular linear system of n equations; (iii)we decrease from O(m~(1.575)n)to O(m~(1.5356)n)the known bound for computing basic solutions to a linear programming problem with m constraints and n variables.  相似文献   

15.
We show that for any pair M,N of n by n M-matrices, the Hadamard (entry-wise) product M°N -1 is again an M-matrix. For a single M-matrix M, the matrix M°M -1 is also considered.  相似文献   

16.
The problem of finding thekth smallest ofn elements can be solved either with O(n) algorithms or with O(n 2) algorithms. Although they require a higher number of operations in the worst case, O(n 2) algorithms are generally preferred to O(n) algorithms because of their better average performance. We present a hybrid algorithm which is O(n) in the worst case and efficient in the average case.  相似文献   

17.
Summary Algorithms are presented which compute theQR factorization of a block-Toeplitz matrix inO(n) 2 block-operations, wheren is the block-order of the matrix and a block-operation is a multiplication, inversion or a set of Householder operations involving one or two blocks. The algorithms are in general analogous to those presented in the scalar Toeplitz case in a previous paper, but the basic operation is the Householder transform rather than the Givens transform, and the computation of the Householder coefficients and other working matrices requires special treatment. Two algorithms are presented-the first computes onlyR explicitly and the second computes bothQ andR.  相似文献   

18.
Summary The solution of systems of linear equations with Hankel coefficient matrices can be computed with onlyO(n 2) arithmetic operations, as compared toO(n 3) operations for the general cases. However, the classical Hankel solvers require the nonsingularity of all leading principal submatrices of the Hankel matrix. The known extensions of these algorithms to general Hankel systems can handle only exactly singular submatrices, but not ill-conditioned ones, and hence they are numerically unstable. In this paper, a stable procedure for solving general nonsingular Hankel systems is presented, using a look-ahead technique to skip over singular or ill-conditioned submatrices. The proposed approach is based on a look-ahead variant of the nonsymmetric Lanczos process that was recently developed by Freund, Gutknecht, and Nachtigal. We first derive a somewhat more general formulation of this look-ahead Lanczos algorithm in terms of formally orthogonal polynomials, which then yields the look-ahead Hankel solver as a special case. We prove some general properties of the resulting look-ahead algorithm for formally orthogonal polynomials. These results are then utilized in the implementation of the Hankel solver. We report some numerical experiments for Hankel systems with ill-conditioned submatrices.The research of the first author was supported by DARPA via Cooperative Agreement NCC 2-387 between NASA and the Universities Space Research Association (USRA).The research of the second author was supported in part by NSF grant DRC-8412314 and Cooperative Agreement NCC 2-387 between NASA and the Universities Space Research Association (USRA).  相似文献   

19.
A heuristic for decomposing traffic matrices in TDMA satellite communication. With the time-division multiple access (TDMA) technique in satellite communication the problem arises to decompose a givenn×n traffic matrix into a weighted sum of a small number of permutation matrices such that the sum of the weights becomes minimal. There are polynomial algorithms when the number of permutation matrices in a decomposition is allowed to be as large asn 2. When the number of matrices is restricted ton, the problem is NP-hard. In this paper we propose a heuristic based on a scaling technique which for each number of allowed matrices in the range fromn ton 2 allows to give a performance guarantee with respect to the total weight of the solution. As a subroutine we use new heuristic methods for decomposing a matrix of small integers into as few matrices as possible without exceeding the lower bound on the total weight. Computational results indicate that the method might also be practical.This work was supported by the Fonds zur Förderung der wissenschaftlichen Forschung, Project S32/01.  相似文献   

20.
A parallel algorithm for depth-first searching of a directed acyclic graph (DAG) on a shared memory model of a SIMD computer is proposed. The algorithm uses two parallel tree traversal algorithms, one for the preorder traversal and the other for therpostorder traversal of an ordered tree. Each of these traversal algorithms has a time complexity ofO(logn) whenO(n) processors are used,n being the number of vertices in the tree. The parallel depth-first search algorithm for a directed acyclic graphG withn vertices has a time complexity ofO((logn)2) whenO(n 2.81/logn) processors are used.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号