122864423
Numerical Computation of the Matrix Exponential with Accuracy Estimate
This paper presents and analyzes an algorithm for computing the exponential of an arbitrary $n \times n$ matrix. Diagonal Pade table approximations are used in conjunction with several techniques for reducing the norm of the matrix. An important feature of the algorithm is that an estimate for the minimum number of digits accurate in the norm of the computed exponential matrix is returned to the user. In obtaining this estimate, several interesting results concerning rounding errors and Pade approximations are presented.
57087721
EZVIDEO, FORTRAN graphics routines for the IBM AT
A set of IBM PC-based FORTRAN plotting routines called EZVIDEO is described in this report. These routines are written in FORTRAN and can be called from FORTRAN programs. EZVIDEO simulates a subset of the well-known DISSPLA graphics calls and makes plots directly on the IBM AT display screen. Screen dumps can also be made to an attached LaserJet or Epson printer to make hard copy without using terminal emulators. More than forty DISSPLA calls are simulated by the EZVIDEO routines. Typical screen plots require about 10 seconds (s), and good hard copy of the screen image on a laser printer requires less than 2 minutes (min). This higher-resolution hard copy is adequate for most purposes because of the enhanced resolution of the screen in the EGA and VGA modes. These EZVIDEO routines give the IB, AT user a stand-alone capability to make useful scientific or engineering plots directly on the AT, using data generated in FORTRAN programs. The routines will also work on the IBM PC or XT in CGA mode, but they require more time and yield less resolution. 7 refs., 4 figs.
120013608
Computing the singular value decompostion of a product of two matrices
An algorithm is developed for computing the singular value decomposition of a product of two general matrices without explicitly forming the product. The algorithm is based on an earlier Jacobi-like method due to Kogbetliantz and uses plane rotations applied to the two matrices separately. A triangular variant of the basic algorithm is developed that reduces the amount of work required.
5786909
The QR algorithm and Hyman’s method on vector computers
The implementation on vector computers of the QR algorithm and of iterative schemes based on obtaining the determinant and its derivatives by Hyman's method are presented. It is shown that iterative schemes based on Hyman's method will probably be more efficient than the QR algorithm on vector computers for large matrices. A theoretical comparison of the Laguerre iterative scheme with the QR algorithm is presented using the latest available CDC STAR-100 instruction execution times. In addition, the results of several test cases run on the Laguerre-Hyman algorithm on a serial computer are reported.
120828253
Balancing the Generalized Eigenvalue Problem
An algorithm is presented for balancing the A and B matrices prior to computing the eigensystem of the generalized eigenvalue problem $Ax = \lambda Bx$. The three-step algorithm is specifically designed to precede the $QZ$-type algorithms, but improved performance is expected from most eigensystem solvers. Permutations and two-sided diagonal transformations are applied to A and B to produce matrices with certain desirable properties. Test cases are presented to illustrate the improved accuracy of the computed eigenvalues.
119362341
Hopf solitons on the lattice
Hopf solitons in the Skyrme?Faddeev model?S2-valued fields on with Skyrme dynamics?are string-like topological solitons. In this letter, we investigate the analogous lattice objects for S2-valued fields on the cubic lattice with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably similar to that of their continuum counterparts, and they exhibit the same power-law relation E ? cH3/4 between the energy E and the Hopf number H.
120625279
Measurement of the Velocity of Sound in Crystals by Pulsed Neutron Diffraction
The diffraction method of observing elementary excitations in crystals has been applied to the study of one-phonon thermal diffuse scattering from pyrolitic graphite on a high-resolution pulsed neutron diffractometer. The variation of the phase velocity of sound as a function of direction in the crystal has been determined for the out-of-plane modes. This is a quick and efficient method of determining sound velocities in crystals under extreme conditions.
122197255
Integrable Yang–Mills–Higgs equations in three-dimensional de Sitter space–time
This paper describes an integrable Yang–Mills–Higgs system on (2+1)-dimensional de Sitter space–time. It is the curved-space–time analog of the Bogomolnyi equations for monopoles on R3. A number of solutions, of various types, are constructed.
121082057
Completely solvable gauge-field equations in dimension greater than four
Abstract This paper deals with analogues, in higher dimensions, of the self-dual Yang-Mills equations in dim4. Requiring that they be the integrability conditions for a linear system leads to a procedure for constructing their solutions. A partial classification of such equations is given, and three examples in dimension eight are studied in detail.
121880030
Instantons and algebraic geometry
Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsätzeAl forl≧1.