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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*...##
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Finite element simulation of semiconductor devices on multiprocessor computers

1994
*
Parallel Computing
*

We present a new iterative method

doi:10.1016/0167-8191(94)90072-8
fatcat:36zr6wducjdzbpdnwcuprnitzi
*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 ...##
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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. ...

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

1990
*
Parallel Algorithms for Matrix Computations
*

Comparison

doi:10.1137/1.9781611971705.ch3
fatcat:pkjwqy26bfcjneyf76jqebybei
*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. ...##
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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. ...##
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Old And New Algorithms For Toeplitz Systems

1988
*
Advanced Algorithms and Architectures for Signal Processing III
*

In this paper we survey some old, "well known"

doi:10.1117/12.948485
fatcat:a335rtof3vfdtlvmmk35gzi5yi
*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. ...##
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Parallelism and fast solution of linear systems

1990
*
Computers and Mathematics with Applications
*

We review some

doi:10.1016/0898-1221(90)90354-m
fatcat:gce2t3r3vjdcvoss2ui2ov52gu
*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. ...##
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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. ...##
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Parallel algorithms for solving large linear systems

1994
*
Journal of Computational and Applied Mathematics
*

This paper gives a survey

doi:10.1016/0377-0427(94)90302-6
fatcat:dt747bh5ivdwvcdrjse7uqcd2m
*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*. ...##
###
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. ...

##
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Least squares modifications with inverse factorizations: Parallel implications

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. ...

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

1993
*
The International Journal of Supercomputing Applications
*

This article surveys

doi:10.1177/109434209300700203
fatcat:ys4xunhbyjgvhn3diz5kqe4xyi
*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. ...##
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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). ...##
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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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