共查询到20条相似文献,搜索用时 0 毫秒
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An algorithm is developed to generate a class of nonsingular matrics that transform a given nonderogatory Hessenberg matrix to its Routh canonical form by similarity, when the latter exists. 相似文献
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《国际计算机数学杂志》2012,89(11):2462-2476
The algebra of the Kronecker products of matrices is recapitulated using a notation that reveals the tensor structures of the matrices. It is claimed that many of the difficulties that are encountered in working with the algebra can be alleviated by paying close attention to the indices that are concealed beneath the conventional matrix notation. The vectorization operations and the commutation transformations that are common in multivariate statistical analysis alter the positional relationship of the matrix elements. These elements correspond to numbers that are liable to be stored in contiguous memory cells of a computer, which should remain undisturbed. It is suggested that, in the absence of an adequate index notation that enables the manipulations to be performed without disturbing the data, even the most clear-headed of computer programmers is liable to perform wholly unnecessary and time-wasting operations that shift data between memory cells. 相似文献
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Emmanuel Lorin de la Grandmaison Yousef Saad Murilo L. Tiago 《Computer Physics Communications》2005,167(1):7-22
We present an efficient implementation of the computation of the coupling matrix arising in time-dependent density functional theory. The two important aspects involved, solution of Poisson's equation and the assembly of the coupling matrix, are investigated in detail and proper approximations are used. Poisson's equation is solved in the reciprocal space and bounded support of the wave functions are exploited in the numerical integration. Experiments show the new implementation is more efficient by an order of magnitude when compared with a standard real-space code. The method is tested to compute optical spectra of realistic systems with hundreds of atoms from first principles. Details of the formalism and implementation are provided and comparisons with a standard real-space code are reported. 相似文献
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DtiStudio: resource program for diffusion tensor computation and fiber bundle tracking 总被引:13,自引:0,他引:13
Jiang H van Zijl PC Kim J Pearlson GD Mori S 《Computer methods and programs in biomedicine》2006,81(2):106-116
A versatile resource program was developed for diffusion tensor image (DTI) computation and fiber tracking. The software can read data formats from a variety of MR scanners. Tensor calculation is performed by solving an over-determined linear equation system using least square fitting. Various types of map data, such as tensor elements, eigenvalues, eigenvectors, diffusion anisotropy, diffusion constants, and color-coded orientations can be calculated. The results are visualized interactively in orthogonal views and in three-dimensional mode. Three-dimensional tract reconstruction is based on the Fiber Assignment by Continuous Tracking (FACT) algorithm and a brute-force reconstruction approach. To improve the time and memory efficiency, a rapid algorithm to perform the FACT is adopted. An index matrix for the fiber data is introduced to facilitate various types of fiber bundles selection based on approaches employing multiple regions of interest (ROIs). The program is developed using C++ and OpenGL on a Windows platform. 相似文献
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Tensor products of matrices play a very important role in approximation and interpolation. This paper describes a systolic algorithm for tensor products in mesh connected arrays and the closely related hypercube architectures (including the Connection Machine). It is based on a new operator called bullet operator which is a higher dimensional matrix operation. The applications of tensor products to multivariable spline blending approximation as well as graphics/image processing are indicated. 相似文献
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The explicit forms of the eigenvectors of the canonical matrix for controllable multiinput systems and the transformation matrix achieving the diagonal matrix are presented. 相似文献
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Omar Wing 《Journal of Parallel and Distributed Computing》1985,2(2):170-181
A systolic array is proposed which is specifically designed to solve a system of sparse linear equations. The array consists of a number of processing elements connected in a ring. Each processing element has its own content-addressable memory where the nonzero elements of the sparse matrix are stored. Matrix elements to which elementary operations are applied are extracted from the memory by content addressing. The system of equations is solved in a systolic fashion and the solution is obtained in NZ + 5n ? 2 steps, where NZ is the number of nonzero elements along and below the diagonal and n is the number of equations. 相似文献
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R. Glass 《Computer Physics Communications》1978,16(1):11-18
The matrix elements of non-scalar products of two irreducible double tensorial sets of operators, of any order, between arbitrarily L-S coupled, N-electron configurations are expressed as products of two recoupling coefficients and one-particle reduced matrix elements. The formulation developed here should be of wide application in various problems relating to atomic structure. 相似文献
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In this article an efficient algorithm for computation of the manipulator inertia matrix is presented. The algorithm is derived based on Newton's and Euler's laws governing the motion of rigid bodies. Using spatial notations, the algorithm leads to the definition of the composite rigid-body spatial inertia which is a spatial representation of the notion of augmented body. The equations resulting from this algorithm are derived in a coordinate-free form. The choice of the coordinate frame for projection of the coordinate-free equations, that is, the intrinsic equations, is discussed by analyzing the vectors and the tensors involved in the final equations. Previously proposed algorithms, the physical interpretations leading to their derivation, and the redundancy in their computations are analyzed. The developed algorithm achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a suitable choice of coordinate frame for projection of the intrinsic equations. 相似文献
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Using the bat: a six-dimensional mouse for object placement 总被引:1,自引:0,他引:1
Existing strategies for 6-D placement (i.e positioning and orienting) are briefly reviewed. An approach is presented that uses a 6-D variant on the conventional mouse, called the `bat', because it is like a mouse that flies. This device encodes relative position, like the mouse, but delivers data in all six dimensions needed for object placement. The goal is to evaluate the bat to determine how well it is suited to placement operations, which are studied in the context of a hierarchically constructed scene. Two distinct parts of the placement operation, visualization and manipulation, are examined and the hardware and software environment designed as a test for the study are described. Manipulation with the bat, which is discussed in some detail, is judged to be successful 相似文献
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A state-space algorithm is studied which generates the (unique) superoptimal Nehari extension of a general rational matrix $. The procedure is to use a set of all-pass transformations to sequentially minimize each frequency-dependent singular value (of the interpolating function) in a dimension peeling algorithm. These all-pass transformations are determined by the maximal Schmidt pairs of a sequence of Hankel operators. The process terminates when the original problem is reduced to one of rank one; at this stage all the available degrees of freedom have been exhausted. The work is an extension of that by Young (1986) and gives a ‘concrete’ state-space implementation of his operator-theoretic arguments. In addition, bounds are given on the minimum achievable values for s1 ∞ (E) = supωεRSi (E(jω)), i = 1, 2,..., rank (G0), and also the McMillan degree of the final superoptimal extension. Here Si.(.) denotes the ith singular value of a (frequency-dependent) matrix, and the numbering is taken to be in decreasing order of magnitude. The algorithm has the property that it may be stopped after minimizing si ∞ (.),i = 1. 2,...,l< rank (G0) if it continues further it is deemed ‘not worth it’ in some sense. A premature termination of the algorithm carries with it an expected saving in computational effort and a predictable reduction in the degree of the extension. A shortened version of the present work has already appeared in work by Limebeeref al, (1987). 相似文献
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形状上下文特征的最大缺憾在于不具备旋转不变性。为了解决这个问题可以采用二维或一维傅里叶变换来解决,然而这样改进会增加特征提取和匹配的运算时间。鉴于傅里叶变换的对称性,对于改进后的形状上下文特征在特征匹配步骤,提出代价矩阵的快速算法,能够减少运算时间。形状点集匹配的实验结果验证了这种新算法的有效性。 相似文献
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Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques. 相似文献