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International Journal of Computer Mathematics Volume 7, 1979 - Issue 3
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Original Articles

A parallel linear system solver

D.J. Evans Department of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, U.K.
&
M. Hatzopoulos Unit of Applied Mathematics, University of Athens, Athens, Greece
Pages 227-238 | Received 01 Sep 1978, Published online: 20 Mar 2007

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S. Chandra Sekhara Rao. (2008) Computation of eigenvalues of a real matrix. International Journal of Computer Mathematics 85:12, pages 1849-1863.
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David J. Evans. (2004) Parallel strategies for linear systems of equations . International Journal of Computer Mathematics 81:4, pages 417-446.
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M. M. Chawla & R. R. Khazal. (2003) A New Wz Factorization For Parallel Solution Of Tridiagonal Systems. International Journal of Computer Mathematics 80:1, pages 123-131.
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D.J. Evans. (2002) The QIF Singular Value Decomposition Method. International Journal of Computer Mathematics 79:5, pages 637-645.
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Nickolaos M. Missirlis & D.J Evans. (1998) The extrapolated ω-double jacobi (Eω-DOJ) method. International Journal of Computer Mathematics 70:2, pages 131-148.
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R. Abdullah & D.J. Evans. (1998) Communication analysis of the PIE and QIF algorithms on distributed memory architecture. International Journal of Computer Mathematics 67:3-4, pages 293-313.
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Abdelhamid Benaini. (1995) The ww T factorization of dense and sparse matrices. International Journal of Computer Mathematics 56:3-4, pages 219-229.
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PARVAZK. BERZIGYAROV & YURIP. BOGLAEV. (1994) LOGIC DERIVATION OF PARALLEL LINEAR EQUATION SYSTEM SOLVERS WITHIN ELIMINATION STRATEGY. Parallel Algorithms and Applications 4:1-2, pages 21-40.
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S. CHANDRA SEKHARA RAO. (1994) PARALLEL SOLUTION OF THE LINEAR SYSTEMS BY AN ALTERNATE QUADRANT INTERLOCKING FACTORIZATION METHOD∗ . Parallel Algorithms and Applications 4:1-2, pages 1-20.
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D. J. EVANS & P. YALAMOV. (1994) THE QZ ORTHOGONAL DECOMPOSITION METHOD. Parallel Algorithms and Applications 2:4, pages 263-276.
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M. M. Chawla, R. R. Khazal & H. F. Al-Fahd. (1994) A direct incomplete factorization method for parallel solution of tridiagonal linear systems. International Journal of Computer Mathematics 54:3-4, pages 249-259.
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D. J. Evans. (1994) The parallel orthogonal decomposition (POD) of a matrix. International Journal of Computer Mathematics 54:1-2, pages 117-124.
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S. Chandra Sekhara Rao & Mohan K. Kadalbajoo. (1994) On the existence of the new quadrant interlocking factorization for parallel solution of tridiagonal linear systems. International Journal of Computer Mathematics 51:3-4, pages 181-192.
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M. M. Chawla & K. Passi. (1994) A parallel elimination method for the solution of banded linear systems. International Journal of Computer Mathematics 50:3-4, pages 197-201.
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Dušan Caf & David J. Evans. (1993) Computing the U L factorisation by newton's method. International Journal of Computer Mathematics 48:1-2, pages 39-51.
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Mohan K. Kadalbajoo, Pravir K. Dutt & Chandra S. Rao. (1993) Existence of the new quadrant interlocking factorization for parallel solution of tridiagonal linear systems. International Journal of Computer Mathematics 48:1-2, pages 95-103.
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M. M. Chawla, K. Passi & P. N. Shivakumar. (1992) A fast parallel algorithm for the solution of tridiagonal linear systems. International Journal of Computer Mathematics 45:1-2, pages 113-121.
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M. M. Chawla & K. Passi. (1991) A new quadrant interlocking factorization for parallel solution of tridiagonal linear systems. International Journal of Computer Mathematics 39:1-2, pages 99-107.
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M.M. Chawal. (1990) A new folding gaussian elimination algorithm for general linear systems. International Journal of Computer Mathematics 36:3-4, pages 221-238.
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M. Hatzopoulos. (1983) A symmetric parallel linear system solver. International Journal of Computer Mathematics 13:2, pages 133-141.
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J. Shanehchi & D. J. Evans. (1982) Further analysis of the quadrant interlocking factorisation (Q.I.F.) method. International Journal of Computer Mathematics 11:1, pages 49-72.
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D.J. Evans, A. Hadjidimos & D. Noutsos. (1981) The parallel solution of banded linear equations by the new quadrant interlocking factorisation (q.i.f.) method. International Journal of Computer Mathematics 9:2, pages 151-161.
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D.J. Evans & A. Hadjidimos. (1980) A modification of the quadrant interlocking factorisation parallel method. International Journal of Computer Mathematics 8:2, pages 149-166.
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S. Chandra Sekhara Rao, Sarita & Rabia Kamra. (2014) Backward error analysis of Choleski Q.I.F. for the solution of symmetric positive definite linear systems. Applied Mathematics and Computation 226, pages 398-405.
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J. A. J. Hall. (2008) Towards a practical parallelisation of the simplex method. Computational Management Science 7:2, pages 139-170.
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Beata Bylina & Jarosław Bylina. (2009) Influence of Preconditioning and Blocking on Accuracy in Solving Markovian Models. International Journal of Applied Mathematics and Computer Science 19:2, pages 207-217.
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Beata Bylina & Jarosław Bylina. 2008. Computational Science – ICCS 2008. Computational Science – ICCS 2008 983 992 .
Beata Bylina & Jarosław Bylina. 2008. Parallel Processing and Applied Mathematics. Parallel Processing and Applied Mathematics 99 107 .
Georg Heinig & Karla Rost. 2007. The Extended Field of Operator Theory. The Extended Field of Operator Theory 129 146 .
Shiguang Li, Gang Zhou & Dayue Chen. (2005) The WZ algorithm for the eigenvalue problem of complex matrix. Applied Mathematics and Computation 165:2, pages 347-353.
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Georg Heinig & Karla Rost. 2005. Recent Advances in Operator Theory and its Applications. Recent Advances in Operator Theory and its Applications 233 252 .
Georg Heinig & Karla Rost. (2004) Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile. Theoretical Computer Science 315:2-3, pages 453-468.
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Beata Bylina & Jarosław Bylina. 2004. Computational Science - ICCS 2004. Computational Science - ICCS 2004 578 581 .
Georg Heinig & Karla Rost. (2003) New Fast Algorithms for Toeplitz-Plus-Hankel Matrices. SIAM Journal on Matrix Analysis and Applications 25:3, pages 842-857.
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Georg Heinig & Karla Rost. 2002. Toeplitz Matrices and Singular Integral Equations. Toeplitz Matrices and Singular Integral Equations 193 208 .
S.Chandra Sekhara Rao. (1997) Existence and uniqueness of WZ factorization. Parallel Computing 23:8, pages 1129-1139.
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P. Yalamov & D.J. Evans. (1995) The WZ matrix factorisation method. Parallel Computing 21:7, pages 1111-1120.
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R Asenjo, M Ujaldón & E.L Zapata. (1993) Parallel WZ factorization on mesh multiprocessors. Microprocessing and Microprogramming 38:1-5, pages 319-326.
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J. Dewor, M. Drescher, T. Klinkenberg & U. Katschner. 1992. Parallele Datenverarbeitung mit dem Transputer. Parallele Datenverarbeitung mit dem Transputer 116 123 .
I García, J.J Merelo, J.D Bruguera & E.L Zapata. (1990) Parallel quadrant interlocking factorization on hypercube computers. Parallel Computing 15:1-3, pages 87-100.
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D. A. Barry. (1990) Supercomputers and their use in modeling subsurface solute transport. Reviews of Geophysics 28:3, pages 277.
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D.J. Evans & G.M. Megson. (1989) Fast triangularization of a symmetric tridiagonal matrix. Journal of Parallel and Distributed Computing 6:3, pages 663-678.
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C.J. Demeure & L.L. Scharf. (1989) Fast algorithms to QR factor circulant matrices. Fast algorithms to QR factor circulant matrices.
C.J. Demeure. (1989) Bowtie factors of Toeplitz matrices by means of split algorithms. IEEE Transactions on Acoustics, Speech, and Signal Processing 37:10, pages 1601-1603.
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R. V. Helgason, J. L. Kennington & H. A. Zaki. (1988) A parallelization of the simplex method. Annals of Operations Research 14:1, pages 17-40.
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D.J. Evans & M.P. Bekakos. (1988) The solution of linear systems by the QIF algorithm on a wavefront array processor. Parallel Computing 7:1, pages 111-130.
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M. Hatzopoulos & D.J. Evans. (1988) Comments on the paper “a short proof for the existence of the WZ-factorization”. Parallel Computing 6:2, pages 259.
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A. Stafylopatis & A. Drigas. 1988. Supercomputing. Supercomputing 994 1010 .
N. M. Missirlis & F. Tjaferis. 1988. Supercomputing. Supercomputing 926 938 .
D.J. Evans. (1987) Parallel Algorithms for Large Scale Linear Systems. IFAC Proceedings Volumes 20:5, pages 19-26.
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D. J. Evans. 1986. Parallel Processing Techniques for Simulation. Parallel Processing Techniques for Simulation 123 142 .
James M. Ortega & Robert G. Voigt. (1985) Solution of Partial Differential Equations on Vector and Parallel Computers. SIAM Review 27:2, pages 149-240.
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M. Hatzopoulos & N.M. Missirlis. (1985) Advantages for solving linear systems in an asynchronous environment. Journal of Computational and Applied Mathematics 12-13, pages 331-340.
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Nikolaos M. Missirlis. (1985) A parallel iterative system solver. Linear Algebra and its Applications 65, pages 25-44.
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R.J. MELOSH, SENOL UTKU & MOKTAR SALAMA. 1985. Advances and Trends in Structures and Dynamics. Advances and Trends in Structures and Dynamics 99 105 .
R.J. Melosh, Senol Utku & Moktar Salama. (1985) Direct finite element equation solving algorithms. Computers & Structures 20:1-3, pages 99-105.
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Jozef Mikloško & Vadim Evgenich Kotov. 1984. Algorithms, Software and Hardware of Parallel Computers. Algorithms, Software and Hardware of Parallel Computers 45 63 .
V. N. Faddeeva & D. K. Faddeev. (1983) Parallel computations in linear algebra. II. Cybernetics 18:3, pages 288-304.
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M. Feilmeier & W. Rönsch. 1982. New Advances in Distributed Computer Systems. New Advances in Distributed Computer Systems 379 393 .
D.J. Evans, A. Hadjidimos & D. Noutsos. (1981) Parallel solution of linear systems by quadrant interlocking factorisation methods. Computer Methods in Applied Mechanics and Engineering 29:1, pages 97-107.
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D.J. Evans & A. Hadjidimos. (1981) Parallel solution to certain banded, symmetric and centro-symmetric systems by using the quadrant interlocking factorisation method. Mathematics and Computers in Simulation 23:2, pages 180-187.
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J. Shanehchi & D. J. Evans. 1981. Conpar 81. Conpar 81 493 507 .
Ladislav Halada. 1981. Conpar 81. Conpar 81 433 440 .
U. Schendel. 1981. Conpar 81. Conpar 81 373 394 .

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