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Page 2360 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
Coleman, A parallel triangu- lar solver for a hypercube multiprocessor (pp. 539-551); C. H. Romine, The parallel solution of triangular systems on a hyper- cube (pp. 552-559); S.  ...  Laub, Implementation of two control system design algorithms on a message-passing hypercube (pp. 512-519); Lothar Reichel, Parallel iterative methods for the solution of Fredholm integral equations of  ... 

Finite element simulation of semiconductor devices on multiprocessor computers

T.F. Pena, E.L. Zapata, D.J. Evans
1994 Parallel Computing  
We present a new iterative method for the solution using finite elements of the non linear Poisson equation and use a Conjugate Gradient type method for solving the non symmetric continuity equations.  ...  We study the distribution of an irregular mesh of triangular elements over a hypercube and the later parallelization of the resolution method.  ...  For solving a linear system of the form A. x = b, where A is an nonsymmetric matrix, the scheme for the unpreconditioned Bi-CGSTAB algorithm is UNPRECONDITIONED BI-CGSTAB ALGORITHM. x 0 is an initial guess  ... 
doi:10.1016/0167-8191(94)90072-8 fatcat:36zr6wducjdzbpdnwcuprnitzi

Page 5861 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
The topics include methods for solving linear systems (including triangular systems with band structure, parallel Gauss elimination, Jacobi, Gauss- Seidel and SOR iterations), parallelization of standard  ...  Nikolaev, Application of the fast Fourier transform to the solution of a seven-point equation on a triangular grid (pp. 43-51); I. E.  ... 

3. A Bibliography on Parallel and Vector Numerical Algorithms [chapter]

James M. Ortega, Robert G. Voigt, Charles H. Romine
1990 Parallel Algorithms for Matrix Computations  
Comparison of methods and algorithms for tridiagonal systems and for vecton'zation of dzfusion computation, in Numrich [1462], pp. 29-56. [4] W . ABU-SUFAH A N D A . MALONY [1986].  ...  Vectorization of a penalty function algorithm for well scheduling, in Gary [3] I. ABU-SHOMAYS [1985].  ...  Solving systems of large dense linear equations, J . Supercomputing, 1, pp. 291-300. [795] R. GRIMES AND H. SIMON [1987]. Dynamic analysis with the Lanczos algorithm on the SCS- 40, Tech.  ... 
doi:10.1137/1.9781611971705.ch3 fatcat:pkjwqy26bfcjneyf76jqebybei

Page 5116 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Bohme, A linear systolic array for the adaptive MVDR beam- former (705-711); Zahari Zlatev, Solving band systems of linear equations by iterative methods on vector machines (713-725).  ...  Nai Kuan Tsao, Solving triangular system in parallel is accurate (633-637); Robert A. van de Geijn, Storage schemes for parallel eigenvalue algorithms (639-647); M. C. A. van Dijke, H.  ... 

Old And New Algorithms For Toeplitz Systems

Richard P. Brent, Franklin T. Luk
1988 Advanced Algorithms and Architectures for Signal Processing III  
In this paper we survey some old, "well known" algorithms and some recent algorithms for solving these problems.  ...  We concentrate our attention on algorithms which can be implemented efficiently on a variety of parallel machines (including pipelined vector processors and systolic arrays).  ...  The development of good parallel algorithms which solve the Toeplitz system (1) in time O((log n) 2 ) on a hypercube, using only a moderate number of processors (say O(n 2 )). 4.  ... 
doi:10.1117/12.948485 fatcat:a335rtof3vfdtlvmmk35gzi5yi

Parallelism and fast solution of linear systems

B. Codenotti, M. Leoncini
1990 Computers and Mathematics with Applications  
We review some of the most important results in the area of fast parallel algorithms for the solution of linear systems and related problems, such as matrix inversion, computation of the determinant and  ...  of the adjoint matrix.  ...  Iterative algorithms on hypercubes Solving a system of linear equations whose coefficient matrix is large and sparse is a case well suited for iterative methods.  ... 
doi:10.1016/0898-1221(90)90354-m fatcat:gce2t3r3vjdcvoss2ui2ov52gu

Page 2697 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Inf. 1 (1995), no. 2, 434-450 (electronic) Summary: “In this article a new parallel iterative algorithm for solving large systems of linear equations is presented.  ...  Comput. 7 (1986), no. 3, 856-869; MR 87g:65064] is one of the most popular iterative methods for the solution of large linear systems of equations Ax = b with a nonsymmetric and sparse matrix.  ... 

Page 2246 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
We show how one algorithm for solving time dependent partial differential equations, local uniform mesh refinement, can be implemented on a multiprocessor system.  ...  (I-CNR-El) The bit-cost of some algorithms for the solution of linear systems. Comput. Math. Appl. 15 (1988), no. 11, 933-937.  ... 

Parallel algorithms for solving large linear systems

T.J. Dekker, W. Hoffmann, K. Potma
1994 Journal of Computational and Applied Mathematics  
This paper gives a survey of research on parallel implementation of various direct methods to solve dense linear systems.  ...  The solution of linear systems continues to play an important role in scientific computing.  ...  system of complex linear equations.  ... 
doi:10.1016/0377-0427(94)90302-6 fatcat:dt747bh5ivdwvcdrjse7uqcd2m

Page 6623 of Mathematical Reviews Vol. , Issue 88m [page]

1988 Mathematical Reviews  
the need for decomposing the system equations.  ...  Summary: “We introduce a graph-theoretic approach to analyse the performances of several parallel Gaussian-like triangularization algorithms on an MIMD computer.  ... 

Least squares modifications with inverse factorizations: Parallel implications

C.-T. Pan, R.J. Plemmons
1989 Journal of Computational and Applied Mathematics  
The process of modifying least squares computations by updating the covariance matrix has been used in control and signal processing for some time in the context of linear sequential filtering.  ...  We have attempted to provide some new insights into least squares modification processes and to suggest parallel algorithms for implementing Kalman type sequential filters in the analysis and solution  ...  Verghese for several helpful comments on a preliminary version of this paper presented at the International Conference on Linear Algebra and Applications in Valencia, Spain, September 1987.  ... 
doi:10.1016/0377-0427(89)90363-4 fatcat:7es5utcynrhc3kr6euxaaslk74

Large Dense Numerical Linear Algebra in 1993: the Parallel Computing Influence

Alan Edelman
1993 The International Journal of Supercomputing Applications  
This article surveys the current state of applications of large dense numerical linear algebra and the in uence of parallel computing.  ...  Furthermore, it attempts to crystallize many important ideas that are sometimes misunderstood in the rush to write fast programs.  ...  Donald Truhlar reports solving dense linear systems of size n = 11; 678 as one component of the calculation.  ... 
doi:10.1177/109434209300700203 fatcat:ys4xunhbyjgvhn3diz5kqe4xyi

Page 3704 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Some of the fundamental new al- gorithms may have practical value; for instance, we substantially improve the algorithmic performance of the parallel solution of triangular and Toeplitz linear systems  ...  A well-known method for solving nonsymmetric linear systems uses a generalized minimal residual algorithm (GMRES).  ... 

Page 2823 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
S. (4-LBRO-PL; Loughborough) The parallel strides reduction algorithms for solving tridiagonal linear systems. (English summary) Neural Parallel Sci. Comput. 1 (1993), no. 1, 29-42.  ...  algorithm to solve the Beltrami equation with applications to quasiconformal mappings.  ... 
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