메뉴 건너뛰기




Volumn 7, Issue 5, 2000, Pages 275-317

Almost block diagonal linear systems: Sequential and parallel solution techniques, and applications

Author keywords

Almost block diagonal systems; Boundary value problems; Collocation methods; Direct algorithms; Finite difference methods; Iterative algorithms; Multiple shooting methods; Parallel computing

Indexed keywords


EID: 0034416441     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/1099-1506(200007/08)7:5<275::AID-NLA198>3.0.CO;2-G     Document Type: Article
Times cited : (36)

References (149)
  • 1
    • 0021312568 scopus 로고
    • Staircase matrices and systems
    • Fourer R. Staircase matrices and systems. SIAM Review 1984; 26:1-70.
    • (1984) SIAM Review , vol.26 , pp. 1-70
    • Fourer, R.1
  • 2
    • 0003641574 scopus 로고
    • Springer-Verlag: New York, Software available as the spline toolbox from Mathworks
    • de Boor C. A Practical Guide to Splines, Springer-Verlag: New York, 1978. Software available as the spline toolbox from Mathworks.
    • (1978) A Practical Guide to Splines
    • De Boor, C.1
  • 3
    • 0016929260 scopus 로고
    • Alternate row and column elimination for solving certain linear systems
    • Varah JM. Alternate row and column elimination for solving certain linear systems. SIAM Journal on Numerical Analysis 1976; 13:71-75.
    • (1976) SIAM Journal on Numerical Analysis , vol.13 , pp. 71-75
    • Varah, J.M.1
  • 6
    • 0002861433 scopus 로고
    • An adaptive finite-difference solver for non-linear two-point boundary problems with mild boundary layers
    • Lentini M, Pereyra V. An adaptive finite-difference solver for non-linear two-point boundary problems with mild boundary layers. SIAM Journal on Numerical Analysis 1977; 14:91-111.
    • (1977) SIAM Journal on Numerical Analysis , vol.14 , pp. 91-111
    • Lentini, M.1    Pereyra, V.2
  • 7
    • 84976854739 scopus 로고
    • PASVA3: An adaptive finite difference FORTRAN program for first order nonlinear boundary value problems
    • Springer-Verlag Lecture Notes in Computer Science, Childs B, Scott M, Daniel JW, Denman E, Nelson P. (eds). Springer-Verlag: New York, Code pasva3 is available as d02raf in the NAG Fortran 77 library
    • Lentini M, Pereyra V. PASVA3: An adaptive finite difference FORTRAN program for first order nonlinear boundary value problems. In Springer-Verlag Lecture Notes in Computer Science, Codes for Boundary Value Problems in Ordinary Differential Equations 76 Childs B, Scott M, Daniel JW, Denman E, Nelson P. (eds). Springer-Verlag: New York, 1979; 67-88. Code pasva3 is available as d02raf in the NAG Fortran 77 library.
    • (1979) Codes for Boundary Value Problems in Ordinary Differential Equations , vol.76 , pp. 67-88
    • Lentini, M.1    Pereyra, V.2
  • 10
    • 0003154080 scopus 로고
    • A new basis implementation for a mixed order boundary value solver
    • Code colnew is available from library ode on netlib
    • Bader G, Ascher UM. A new basis implementation for a mixed order boundary value solver. SIAM Journal on Scientific and Statistical Computing 1981; 9:483-500. Code colnew is available from library ode on netlib.
    • (1981) SIAM Journal on Scientific and Statistical Computing , vol.9 , pp. 483-500
    • Bader, G.1    Ascher, U.M.2
  • 11
    • 0022048157 scopus 로고
    • The close relationships between methods for solving two-point boundary value problems
    • Lentini M, Osborne MR, Russell RD. The close relationships between methods for solving two-point boundary value problems. SIAM Journal on Numerical Analysis 1985; 22:280-309.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 280-309
    • Lentini, M.1    Osborne, M.R.2    Russell, R.D.3
  • 12
    • 0013723684 scopus 로고
    • The application of implicit Runge-Kutta and collocation methods to boundary value problems
    • Weiss R. The application of implicit Runge-Kutta and collocation methods to boundary value problems. Mathematics of Computation 1974; 28:449-464.
    • (1974) Mathematics of Computation , vol.28 , pp. 449-464
    • Weiss, R.1
  • 13
    • 0001716997 scopus 로고
    • Some relationships between implicit Runge-Kutta, collocation and Lanczos τ methods and their stability properties
    • Wright K. Some relationships between implicit Runge-Kutta, collocation and Lanczos τ methods and their stability properties. BIT 1970; 20:217-227.
    • (1970) BIT , vol.20 , pp. 217-227
    • Wright, K.1
  • 14
    • 0039485998 scopus 로고
    • Finite Element Galerkin Methods for Differential Equations
    • Marcel Dekker: New York
    • Fairweather G. Finite Element Galerkin Methods for Differential Equations. Lecture in Notes Pure and Applied Mathematics, 34. Marcel Dekker: New York, 1978.
    • (1978) Lecture in Notes Pure and Applied Mathematics , vol.34
    • Fairweather, G.1
  • 15
    • 84976770923 scopus 로고
    • SOLVEBLOK: A package for solving almost block diagonal linear systems
    • de Boor C, Weiss R. SOLVEBLOK: A package for solving almost block diagonal linear systems. ACM Transactions on Mathematical Software 1980; 6:80-87.
    • (1980) ACM Transactions on Mathematical Software , vol.6 , pp. 80-87
    • De Boor, C.1    Weiss, R.2
  • 17
    • 0024937314 scopus 로고
    • Vector- and parallelization of ODE BVP codes
    • Gladwell I, Hay RI. Vector-and parallelization of ODE BVP codes. Parallel Computing 1989; 12:343-350.
    • (1989) Parallel Computing , vol.12 , pp. 343-350
    • Gladwell, I.1    Hay, R.I.2
  • 18
    • 0005729071 scopus 로고
    • PhD thesis, Department of Mathematics, University of Kentucky, Code pabbpack, a parallel implementation of the SLU algorithm of Wright SJ [116], is available by anonymous ftp from directory /pub/karin/pabbpack/ at math.nist.gov. (This version was prepared for parallel processors that are no longer widely available; it uses machine-specific parallel directives.)
    • Bennett KR. Parallel collocation methods for boundary value problems. PhD thesis, Department of Mathematics, University of Kentucky, 1991. Code pabbpack, a parallel implementation of the SLU algorithm of Wright SJ [116], is available by anonymous ftp from directory /pub/karin/pabbpack/ at math.nist.gov. (This version was prepared for parallel processors that are no longer widely available; it uses machine-specific parallel directives.)
    • (1991) Parallel Collocation Methods for Boundary Value Problems
    • Bennett, K.R.1
  • 19
    • 0037710893 scopus 로고
    • A parallel boundary value ODE code for shared-memory machines
    • Code pcolnew is available by anonymous ftp from directory /pub/karin/pcolnew/ at math.nist.gov. (This version was prepared for specific shared memory parallel computers which are no longer widely available.)
    • Bennett KR, Fairweather G. A parallel boundary value ODE code for shared-memory machines. International Journal of High Speed Computing 1992; 4:71-86. Code pcolnew is available by anonymous ftp from directory /pub/karin/pcolnew/ at math.nist.gov. (This version was prepared for specific shared memory parallel computers which are no longer widely available.)
    • (1992) International Journal of High Speed Computing , vol.4 , pp. 71-86
    • Bennett, K.R.1    Fairweather, G.2
  • 20
    • 0038387007 scopus 로고
    • Adaptation of a two-point boundary value problem solver to a vector-multiprocessor environment
    • Wright SJ, Pereyra V. Adaptation of a two-point boundary value problem solver to a vector-multiprocessor environment. SIAM Journal on Scientific and Statistical Computing 1990; 11:425-449.
    • (1990) SIAM Journal on Scientific and Statistical Computing , vol.11 , pp. 425-449
    • Wright, S.J.1    Pereyra, V.2
  • 21
    • 0020304319 scopus 로고
    • High order methods for the numerical solution of two point boundary value problems
    • Cash JR, Singhal A. High order methods for the numerical solution of two point boundary value problems. BIT 1982; 22:184-199.
    • (1982) BIT , vol.22 , pp. 184-199
    • Cash, J.R.1    Singhal, A.2
  • 22
    • 0022791144 scopus 로고
    • The numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections - Part 1 : A survey and comparison of some one step formulae
    • Cash JR. The numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections - Part 1 : A survey and comparison of some one step formulae. Computers and Mathematics with Applications 1986; 12:1029-1048.
    • (1986) Computers and Mathematics with Applications , vol.12 , pp. 1029-1048
    • Cash, J.R.1
  • 23
    • 0000257129 scopus 로고
    • The numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections - Part 2: The development and analysis of highly stable deferred correction formulae
    • Cash JR. The numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections - Part 2: The development and analysis of highly stable deferred correction formulae. SIAM Journal on Numerical Analysis 1988; 25:862-882.
    • (1988) SIAM Journal on Numerical Analysis , vol.25 , pp. 862-882
    • Cash, J.R.1
  • 24
    • 0025596687 scopus 로고
    • Implementation issues in solving nonlinear equations for two-point boundary value problems
    • Cash JR, Wright MH. Implementation issues in solving nonlinear equations for two-point boundary value problems. Computing 1990; 45:17-37.
    • (1990) Computing , vol.45 , pp. 17-37
    • Cash, J.R.1    Wright, M.H.2
  • 25
    • 0000529753 scopus 로고
    • A deferred correction method for nonlinear two-point boundary value problems
    • Code twpbvp available from library ode on netlib
    • Cash JR, Wright MH. A deferred correction method for nonlinear two-point boundary value problems. SIAM Journal on Scientific and Statistical Computing 1991; 12:971-989. Code twpbvp available from library ode on netlib.
    • (1991) SIAM Journal on Scientific and Statistical Computing , vol.12 , pp. 971-989
    • Cash, J.R.1    Wright, M.H.2
  • 26
    • 0022889135 scopus 로고
    • Efficient classes of Runge-Kutta methods for two-point boundary value problems
    • Enright WH, Muir PH. Efficient classes of Runge-Kutta methods for two-point boundary value problems. Computing 1986; 37:315-344.
    • (1986) Computing , vol.37 , pp. 315-344
    • Enright, W.H.1    Muir, P.H.2
  • 27
    • 2142782818 scopus 로고    scopus 로고
    • Runge-Kutta software with defect control for boundary value ODES
    • Enright WH, Muir PH. Runge-Kutta software with defect control for boundary value ODES. SIAM Journal on Scientific Computing 1996; 17:479-497.
    • (1996) SIAM Journal on Scientific Computing , vol.17 , pp. 479-497
    • Enright, W.H.1    Muir, P.H.2
  • 28
    • 0022016199 scopus 로고
    • An adaptive boundary value Runge-Kutta solver for first order boundary value problems
    • Gupta S. An adaptive boundary value Runge-Kutta solver for first order boundary value problems. SIAM Journal on Numerical Analysis 1985; 22:114-126.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 114-126
    • Gupta, S.1
  • 29
    • 0347111987 scopus 로고
    • Implicit Runge-Kutta methods for two-point boundary value problems
    • PhD thesis, University of Toronto, Department of Computer Science
    • Muir PH. Implicit Runge-Kutta methods for two-point boundary value problems. PhD thesis, University of Toronto, Department of Computer Science, Technical Report 175/84, 1984.
    • (1984) Technical Report 175/84
    • Muir, P.H.1
  • 30
    • 0037710896 scopus 로고
    • A parallel implementation of a Runge-Kutta code for systems of nonlinear boundary value ODEs
    • Muir PH, Remington K. A parallel implementation of a Runge-Kutta code for systems of nonlinear boundary value ODEs. Congressus Numerantium 1994; 99:291-305.
    • (1994) Congressus Numerantium , vol.99 , pp. 291-305
    • Muir, P.H.1    Remington, K.2
  • 31
    • 0001242043 scopus 로고
    • Reformulation of boundary value problems into 'standard form'
    • Ascher UM, Russell RD. Reformulation of boundary value problems into 'standard form'. SIAM Review 1981; 23:238-254.
    • (1981) SIAM Review , vol.23 , pp. 238-254
    • Ascher, U.M.1    Russell, R.D.2
  • 32
    • 0000559698 scopus 로고
    • Steady state and periodic solution paths: Their bifurcations and computations
    • Numerical Methods for Bifurcation Problems Küpper T, Mittelmann HD, Weber H. (eds). Birkhäuser: Boston, MA
    • Jepson AD, Keller HB. Steady state and periodic solution paths: their bifurcations and computations. In Numerical Methods for Bifurcation Problems Küpper T, Mittelmann HD, Weber H. (eds). International Series of Numerical Mathematics. 70. Birkhäuser: Boston, MA, 1984; 219-246.
    • (1984) International Series of Numerical Mathematics , vol.70 , pp. 219-246
    • Jepson, A.D.1    Keller, H.B.2
  • 33
    • 21844508391 scopus 로고
    • Computation and parametrization of periodic and connecting orbits
    • Moore G. Computation and parametrization of periodic and connecting orbits. IMA Journal of Numerical Analysis 1995; 15:245-263.
    • (1995) IMA Journal of Numerical Analysis , vol.15 , pp. 245-263
    • Moore, G.1
  • 34
    • 0000264946 scopus 로고
    • Geometric methods for computing invariant manifolds
    • Moore G. Geometric methods for computing invariant manifolds. Applied Numerical Mathematics 1995; 17:311-318.
    • (1995) Applied Numerical Mathematics , vol.17 , pp. 311-318
    • Moore, G.1
  • 35
    • 0001493712 scopus 로고
    • Prediction of membrane separation characteristics by pore distribution measurements and surface force-pore flow model
    • Bhattacharyya D, Jevtitch M, Schrodt JT, Fairweather G. Prediction of membrane separation characteristics by pore distribution measurements and surface force-pore flow model. Chemical Engineering Communications 1986; 42:111-128.
    • (1986) Chemical Engineering Communications , vol.42 , pp. 111-128
    • Bhattacharyya, D.1    Jevtitch, M.2    Schrodt, J.T.3    Fairweather, G.4
  • 36
    • 0000378937 scopus 로고
    • Numerical analysis and control in bifurcation problems, (I) Bifurcations in finite dimensions
    • Doedel E, Keller HB, Kernevez J. Numerical analysis and control in bifurcation problems, (I) Bifurcations in finite dimensions. International Journal of Bifurcation and Chaos 1991; 1:493-520.
    • (1991) International Journal of Bifurcation and Chaos , vol.1 , pp. 493-520
    • Doedel, E.1    Keller, H.B.2    Kernevez, J.3
  • 37
    • 0000378934 scopus 로고
    • Numerical analysis and control in bifurcation problems, (II) Bifurcations in infinite dimensions
    • Doedel E, Keller HB, Kernevez J. Numerical analysis and control in bifurcation problems, (II) Bifurcations in infinite dimensions. International Journal of Bifurcation and Chaos 1992; 2:745-772.
    • (1992) International Journal of Bifurcation and Chaos , vol.2 , pp. 745-772
    • Doedel, E.1    Keller, H.B.2    Kernevez, J.3
  • 38
    • 0003487030 scopus 로고
    • AUTO94: Software for continuation and bifurcation problems in ordinary differential equations
    • Center for Research on Parallel Computing, California Institute of Technology, Code auto94 and a more recent version auto97 are available by contacting the author at doedel@cs.concordia.ca
    • Doedel E, Wang XJ, Fairgrieve TF. AUTO94: software for continuation and bifurcation problems in ordinary differential equations. Technical Report CRPC-95-1, Center for Research on Parallel Computing, California Institute of Technology, 1995. Code auto94 and a more recent version auto97 are available by contacting the author at doedel@cs.concordia.ca.
    • (1995) Technical Report CRPC-95-1
    • Doedel, E.1    Wang, X.J.2    Fairgrieve, T.F.3
  • 40
    • 38248999728 scopus 로고
    • Parallel stable compactification for ODE with parameters and multipoint conditions
    • Mattheij RMM, Wright SJ. Parallel stable compactification for ODE with parameters and multipoint conditions. Applied Numerical Mathematics 1993; 13:305-333.
    • (1993) Applied Numerical Mathematics , vol.13 , pp. 305-333
    • Mattheij, R.M.M.1    Wright, S.J.2
  • 42
    • 0000958123 scopus 로고
    • A new difference scheme for parabolic equations
    • Hubbard B (ed.). Academic Press: New York
    • Keller HB. A new difference scheme for parabolic equations. In Numerical Solution of Differential Equations - II, Hubbard B (ed.). Academic Press: New York, 1971; 327-350.
    • (1971) Numerical Solution of Differential Equations - II , pp. 327-350
    • Keller, H.B.1
  • 43
    • 38249002591 scopus 로고
    • Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions
    • Bialecki B, Fairweather G. Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions. Journal of Computational and Applied Mathematics 1993; 46:369-386.
    • (1993) Journal of Computational and Applied Mathematics , vol.46 , pp. 369-386
    • Bialecki, B.1    Fairweather, G.2
  • 44
    • 0003373869 scopus 로고
    • Matrix decomposition algorithms for orthogonal spline collocation for separable elliptic boundary value problems
    • Bialecki B, Fairweather G. Matrix decomposition algorithms for orthogonal spline collocation for separable elliptic boundary value problems. SIAM Journal on Scientific Computing 1995; 16:330-347.
    • (1995) SIAM Journal on Scientific Computing , vol.16 , pp. 330-347
    • Bialecki, B.1    Fairweather, G.2
  • 45
    • 0026817974 scopus 로고
    • Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations
    • Bialecki B, Fairweather G, Bennett KR. Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations. SIAM Journal on Numerical Analysis 1992; 29:156-173.
    • (1992) SIAM Journal on Numerical Analysis , vol.29 , pp. 156-173
    • Bialecki, B.1    Fairweather, G.2    Bennett, K.R.3
  • 46
    • 38249026426 scopus 로고
    • A fast algorithm for solving the tensor product collocation equations
    • Sun W, Zamani NG. A fast algorithm for solving the tensor product collocation equations. Journal of the Franklin Institute 1989; 326:295-307.
    • (1989) Journal of the Franklin Institute , vol.326 , pp. 295-307
    • Sun, W.1    Zamani, N.G.2
  • 47
    • 0005747435 scopus 로고
    • Fourier matrix decomposition methods for the least squares solution of singular Neumann and periodic Hermite bicubic collocation problems
    • Bialecki B, Remington KA. Fourier matrix decomposition methods for the least squares solution of singular Neumann and periodic Hermite bicubic collocation problems. SIAM Journal on Scientific Computing 1995; 16:431-451.
    • (1995) SIAM Journal on Scientific Computing , vol.16 , pp. 431-451
    • Bialecki, B.1    Remington, K.A.2
  • 48
    • 0005744247 scopus 로고
    • Parallel matrix decomposition algorithms for separable elliptic boundary value problems
    • Computational Techniques and Applications: CTAC-91. Adelaide, South Australia, July 1991, Noye BJ, Benjamin BR, Colgan LH. (eds). Computational Mathematics Group, Australian Mathematical Society, Adelaide, Australia
    • Fairweather G, Bennett KR, Bialecki B. Parallel matrix decomposition algorithms for separable elliptic boundary value problems. In Computational Techniques and Applications: CTAC-91. Proceeding of the 1991 International Conference on Computational Techniques and Applications, Adelaide, South Australia, July 1991, Noye BJ, Benjamin BR, Colgan LH. (eds). Computational Mathematics Group, Australian Mathematical Society, Adelaide, Australia, 1992; 63-74.
    • (1992) Proceeding of the 1991 International Conference on Computational Techniques and Applications , pp. 63-74
    • Fairweather, G.1    Bennett, K.R.2    Bialecki, B.3
  • 49
    • 21844490490 scopus 로고
    • A high order direct method for solving Poisson's equation in a disc
    • Sun W. A high order direct method for solving Poisson's equation in a disc. Numerische Mathematik 1995; 70:501-506.
    • (1995) Numerische Mathematik , vol.70 , pp. 501-506
    • Sun, W.1
  • 50
    • 0005729075 scopus 로고
    • Fast three-dimensional elliptic solvers on distributed network clusters
    • Joubert GR, Trystram D, Peters FJ, Evans DJ. (eds). Elsevier, Amsterdam
    • Pozo R, Remington K. Fast three-dimensional elliptic solvers on distributed network clusters. In Parallel Computing: Trends and Applications, Joubert GR, Trystram D, Peters FJ, Evans DJ. (eds). Elsevier, Amsterdam, 1994; 201-208.
    • (1994) Parallel Computing: Trends and Applications , pp. 201-208
    • Pozo, R.1    Remington, K.2
  • 51
    • 0032270721 scopus 로고    scopus 로고
    • Fast algorithms for high-order spline collocation systems
    • Sun W. Fast algorithms for high-order spline collocation systems. Numerische Mathematik 1998; 81:143-160.
    • (1998) Numerische Mathematik , vol.81 , pp. 143-160
    • Sun, W.1
  • 52
    • 0005683761 scopus 로고
    • An alternating direction implicit method for orthogonal spline collocation linear systems
    • Bialecki B. An alternating direction implicit method for orthogonal spline collocation linear systems. Numerische Mathematik 1991; 59:413-429.
    • (1991) Numerische Mathematik , vol.59 , pp. 413-429
    • Bialecki, B.1
  • 53
    • 0027308043 scopus 로고
    • Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation
    • Cooper KD. Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation. Numerical Methods for Partial Differential Equations 1993; 9:93-106.
    • (1993) Numerical Methods for Partial Differential Equations , vol.9 , pp. 93-106
    • Cooper, K.D.1
  • 56
    • 0026169773 scopus 로고
    • Alternating direction collocation for separable elliptic partial differential equations
    • Cooper KD, Prenter PM. Alternating direction collocation for separable elliptic partial differential equations. SIAM Journal on Numerical Analysis 1991; 28:711-727.
    • (1991) SIAM Journal on Numerical Analysis , vol.28 , pp. 711-727
    • Cooper, K.D.1    Prenter, P.M.2
  • 57
    • 0023287845 scopus 로고
    • Tensor product generalized ADI methods for separable elliptic problems
    • Dyksen WR. Tensor product generalized ADI methods for separable elliptic problems. SIAM Journal on Numerical Analysis 1987; 24:59-76.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , pp. 59-76
    • Dyksen, W.R.1
  • 58
    • 0005653928 scopus 로고
    • Iterative algorithms for orthogonal spline collocation linear systems
    • Sun W. Iterative algorithms for orthogonal spline collocation linear systems. SIAM Journal on Scientific Computing 1995; 16:720-737.
    • (1995) SIAM Journal on Scientific Computing , vol.16 , pp. 720-737
    • Sun, W.1
  • 59
    • 0001668904 scopus 로고    scopus 로고
    • Block iterative algorithms for solving Hermite bicubic collocation equations
    • Sun W. Block iterative algorithms for solving Hermite bicubic collocation equations. SIAM Journal on Numerical Analysis 1996; 33:589-601.
    • (1996) SIAM Journal on Numerical Analysis , vol.33 , pp. 589-601
    • Sun, W.1
  • 60
    • 0005653924 scopus 로고
    • Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation
    • Bialecki B. Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation. Numerical Algorithms 1994; 8:167-184.
    • (1994) Numerical Algorithms , vol.8 , pp. 167-184
    • Bialecki, B.1
  • 63
    • 0032334010 scopus 로고    scopus 로고
    • Orthogonal spline collocation methods for biharmonic problems
    • Lou Z, Bialecki B, Fairweather G. Orthogonal spline collocation methods for biharmonic problems. Numerische Mathematik 1998; 80:267-303.
    • (1998) Numerische Mathematik , vol.80 , pp. 267-303
    • Lou, Z.1    Bialecki, B.2    Fairweather, G.3
  • 64
    • 0027891708 scopus 로고
    • Orthogonal collocation solution of biharmonic equations
    • Sun W. Orthogonal collocation solution of biharmonic equations. International Journal of Computer Mathematics 1993; 49:221-232.
    • (1993) International Journal of Computer Mathematics , vol.49 , pp. 221-232
    • Sun, W.1
  • 65
    • 0030123372 scopus 로고    scopus 로고
    • High performance solution of partial differential equations discretized using a Chebyshev spectral collocation method
    • Cyphers C, Paprzycki M, Karageorghis A. High performance solution of partial differential equations discretized using a Chebyshev spectral collocation method. Journal of Computational and Applied Mathematics 1996; 69:71-80.
    • (1996) Journal of Computational and Applied Mathematics , vol.69 , pp. 71-80
    • Cyphers, C.1    Paprzycki, M.2    Karageorghis, A.3
  • 66
    • 0026947436 scopus 로고
    • The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method
    • Karageorghis A. The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method. Computer Methods in Applied Mechanics and Engineering 1992; 100:339-358.
    • (1992) Computer Methods in Applied Mechanics and Engineering , vol.100 , pp. 339-358
    • Karageorghis, A.1
  • 67
    • 21344436757 scopus 로고    scopus 로고
    • An efficient direct method for fully conforming spectral collocation schemes
    • Karageorghis A, Paprzycki M. An efficient direct method for fully conforming spectral collocation schemes. Numerical Algorithms 1996; 12:309-319.
    • (1996) Numerical Algorithms , vol.12 , pp. 309-319
    • Karageorghis, A.1    Paprzycki, M.2
  • 69
    • 40249103125 scopus 로고
    • Collocation Methods for Parabolic Equations in a Single Space Variable
    • Springer-Verlag: New York
    • Douglas Jr. J, Dupont T. Collocation Methods for Parabolic Equations in a Single Space Variable. Lecture Notes in Mathematics, 385. Springer-Verlag: New York, 1974.
    • (1974) Lecture Notes in Mathematics , vol.385
    • Douglas Jr., J.1    Dupont, T.2
  • 70
    • 34250280847 scopus 로고
    • A note on the efficient implementation of certain Fade methods for linear parabolic problems
    • Fairweather G. A note on the efficient implementation of certain Fade methods for linear parabolic problems. BIT 1978; 18:106-109.
    • (1978) BIT , vol.18 , pp. 106-109
    • Fairweather, G.1
  • 72
    • 84968468426 scopus 로고
    • Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles
    • Bialecki B, Fernandes RI. Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles. Mathematics of Computation 1993; 60:545-573.
    • (1993) Mathematics of Computation , vol.60 , pp. 545-573
    • Bialecki, B.1    Fernandes, R.I.2
  • 73
    • 0001439276 scopus 로고    scopus 로고
    • An orthogonal spline collocation alternating direction implicit Crank-Nicolson method for linear parabolic problems on rectangles
    • Bialecki B, Fernandes RI. An orthogonal spline collocation alternating direction implicit Crank-Nicolson method for linear parabolic problems on rectangles. SIAM Journal on Numerical Analysis 1999; 36:1414-1434
    • (1999) SIAM Journal on Numerical Analysis , vol.36 , pp. 1414-1434
    • Bialecki, B.1    Fernandes, R.I.2
  • 75
    • 0031534190 scopus 로고    scopus 로고
    • Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles
    • Fernandes RI. Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles. Numerische Mathematik 1997; 77:223-241.
    • (1997) Numerische Mathematik , vol.77 , pp. 223-241
    • Fernandes, R.I.1
  • 76
    • 0027559394 scopus 로고
    • Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables
    • Fernandes RI, Fairweather G. Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables. Numerical Methods for Partial Differential Equations 1993; 9:191-211.
    • (1993) Numerical Methods for Partial Differential Equations , vol.9 , pp. 191-211
    • Fernandes, R.I.1    Fairweather, G.2
  • 77
    • 0001567661 scopus 로고    scopus 로고
    • Discrete-time orthogonal spline collocation schemes for Schrödinger equations in two space variables
    • Li B, Fairweather B, Bialecki B. Discrete-time orthogonal spline collocation schemes for Schrödinger equations in two space variables. SIAM Journal on Numerical Analysis 1998; 35:453-477.
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , pp. 453-477
    • Li, B.1    Fairweather, B.2    Bialecki, B.3
  • 78
    • 0005755167 scopus 로고    scopus 로고
    • Discrete-time orthogonal spline collocation schemes for vibration problems
    • Department of Mathematical and Computer Sciences, Colorado School of Mines
    • Li B, Fairweather G, Bialecki B. Discrete-time orthogonal spline collocation schemes for vibration problems. Technical Report 00-05, Department of Mathematical and Computer Sciences, Colorado School of Mines, 2000.
    • (2000) Technical Report 00-05
    • Li, B.1    Fairweather, G.2    Bialecki, B.3
  • 79
    • 0005728294 scopus 로고
    • Orthogonal spline collocation solution of nonlinear Schrödinger equations
    • Mathematics of Computation 1943-1993: a half-century of computational mathematics, American Mathematical Society: Providence RI
    • Robinson MP. Orthogonal spline collocation solution of nonlinear Schrödinger equations. In Mathematics of Computation 1943-1993: a half-century of computational mathematics, Proceedings of the Symposium on Applied Mathematics, 48. American Mathematical Society: Providence RI, 1994; 355-360.
    • (1994) Proceedings of the Symposium on Applied Mathematics , vol.48 , pp. 355-360
    • Robinson, M.P.1
  • 80
    • 0031117895 scopus 로고    scopus 로고
    • The solution of nonlinear Schrödinger equations using orthogonal spline collocation
    • Corrigendum: Computers and Mathematics with Applications 1998; 35:151
    • Robinson MP. The solution of nonlinear Schrödinger equations using orthogonal spline collocation. Computers and Mathematics with Applications 1997; 33;39-57. [Corrigendum: Computers and Mathematics with Applications 1998; 35:151].
    • (1997) Computers and Mathematics with Applications , vol.33 , pp. 39-57
    • Robinson, M.P.1
  • 81
    • 0005664185 scopus 로고
    • An orthogonal spline collocation method for the numerical solution of underwater acoustic wave propagation problems
    • Lee D, Vichnevetsky R, Robinson AR. (eds). Elsevier: Amsterdam
    • Robinson MP, Fairweather G. An orthogonal spline collocation method for the numerical solution of underwater acoustic wave propagation problems. In Computational Acoustics, vol. 2, Lee D, Vichnevetsky R, Robinson AR. (eds). Elsevier: Amsterdam, 1993;339-353.
    • (1993) Computational Acoustics , vol.2 , pp. 339-353
    • Robinson, M.P.1    Fairweather, G.2
  • 82
    • 0001313931 scopus 로고
    • Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems
    • Robinson MP, Fairweather G. Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems. Journal of Computational Acoustics 1993; 1:355-370.
    • (1993) Journal of Computational Acoustics , vol.1 , pp. 355-370
    • Robinson, M.P.1    Fairweather, G.2
  • 83
    • 21844508595 scopus 로고
    • Orthogonal spline collocation methods for Schrödinger-type problems in one space variable
    • Robinson MP, Fairweather G. Orthogonal spline collocation methods for Schrödinger-type problems in one space variable. Numerische Mathematik 1994; 68:355-376.
    • (1994) Numerische Mathematik , vol.68 , pp. 355-376
    • Robinson, M.P.1    Fairweather, G.2
  • 84
    • 0032021197 scopus 로고    scopus 로고
    • Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation
    • Manickam AV, Moudgalya KM, Pani AK. Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation. Computers and Mathematics with Applications 1998; 35:5-25.
    • (1998) Computers and Mathematics with Applications , vol.35 , pp. 5-25
    • Manickam, A.V.1    Moudgalya, K.M.2    Pani, A.K.3
  • 85
    • 0000397513 scopus 로고    scopus 로고
    • A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation
    • Manickam SAV, Pani AK, Chung SK. A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation. Numerical Methods for Partial Differential Equations 1998; 14:695-716.
    • (1998) Numerical Methods for Partial Differential Equations , vol.14 , pp. 695-716
    • Manickam, S.A.V.1    Pani, A.K.2    Chung, S.K.3
  • 86
    • 0001683045 scopus 로고
    • The reformulation and numerical solution of certain nonclassical initial-boundary value problems
    • Fairweather G, Saylor RD. The reformulation and numerical solution of certain nonclassical initial-boundary value problems. SIAM Journal on Scientific and Statistical Computing 1991; 12:127-144.
    • (1991) SIAM Journal on Scientific and Statistical Computing , vol.12 , pp. 127-144
    • Fairweather, G.1    Saylor, R.D.2
  • 90
    • 0020822005 scopus 로고
    • FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination
    • Diaz JC, Fairweather G, Keast P. FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. ACM Transactions on Mathematical Software 1983; 9:358-375.
    • (1983) ACM Transactions on Mathematical Software , vol.9 , pp. 358-375
    • Diaz, J.C.1    Fairweather, G.2    Keast, P.3
  • 92
    • 84976658278 scopus 로고
    • Algorithm 603:. COLROW and ARCECO: FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination
    • Diaz JC, Fairweather G, Keast P. Algorithm 603:. COLROW and ARCECO: FORTRAN packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination. ACM Transactions on Mathematical Software 1983; 9:376-380.
    • (1983) ACM Transactions on Mathematical Software , vol.9 , pp. 376-380
    • Diaz, J.C.1    Fairweather, G.2    Keast, P.3
  • 93
    • 0038387014 scopus 로고
    • Codes for almost block diagonal systems
    • Code f01lhf is available in the NAG Fortran 77 library
    • Brankin RW, Gladwell I. Codes for almost block diagonal systems. Computers and Mathematics with Applications 1990; 19:1-6. Code f01lhf is available in the NAG Fortran 77 library.
    • (1990) Computers and Mathematics with Applications , vol.19 , pp. 1-6
    • Brankin, R.W.1    Gladwell, I.2
  • 94
    • 0023983122 scopus 로고
    • An extended set of FORTRAN basic linear algebra subprograms
    • The level 2 BIAS are available on netlib, in the NAG libraries, and, in optimized form, from many computer manufacturers
    • Dongarra J, Du Croz J, Hammarling S, Hanson RJ. An extended set of FORTRAN basic linear algebra subprograms. ACM Transactions on Mathematical Software 1988; 14:1-17. The level 2 BIAS are available on netlib, in the NAG libraries, and, in optimized form, from many computer manufacturers.
    • (1988) ACM Transactions on Mathematical Software , vol.14 , pp. 1-17
    • Dongarra, J.1    Du Croz, J.2    Hammarling, S.3    Hanson, R.J.4
  • 95
    • 0041391346 scopus 로고
    • A set of level 3 basic linear algebra subprograms
    • Argonne National Laboratory, The level 3 BIAS are available on netlib, in the NAG libraries, and, in optimized form, from many computer manufacturers
    • Dongarra J, Du Croz J, Hammarling S. A set of level 3 basic linear algebra subprograms. Technical Report ANL-MCS-TM57, Argonne National Laboratory, 1988. The level 3 BIAS are available on netlib, in the NAG libraries, and, in optimized form, from many computer manufacturers.
    • (1988) Technical Report ANL-MCS-TM57
    • Dongarra, J.1    Du Croz, J.2    Hammarling, S.3
  • 96
    • 0027911840 scopus 로고
    • Parallel solution of almost block diagonal systems on the CRAY Y-MP using level 3 BLAS
    • Gladwell I, Paprzycki M. Parallel solution of almost block diagonal systems on the CRAY Y-MP using level 3 BLAS. Journal of Computational and Applied Mathematics 1993; 45:181-189.
    • (1993) Journal of Computational and Applied Mathematics , vol.45 , pp. 181-189
    • Gladwell, I.1    Paprzycki, M.2
  • 98
    • 3042884799 scopus 로고
    • A level 3 BLAS based solver for almost block diagonal systems
    • Department of Mathematics, Southern Methodist University, Code l3abdsol is available from library linalg on netlib
    • Cyphers C, Paprzycki M. A level 3 BLAS based solver for almost block diagonal systems. SMU Softreport 92-3, Department of Mathematics, Southern Methodist University, 1992. Code l3abdsol is available from library linalg on netlib.
    • (1992) SMU Softreport 92-3
    • Cyphers, C.1    Paprzycki, M.2
  • 99
    • 85037483766 scopus 로고    scopus 로고
    • Code transcolrow.f [1997]
    • Keast P. Code transcolrow.f is available at http://www.mscs.dal.ca/~keast/leq/ [1997].
    • Keast, P.1
  • 100
    • 85037459233 scopus 로고    scopus 로고
    • Code complexcolrow.f [1997]
    • Keast P. Code complexcolrow.f is available at http://www.mscs.dal.ca/~keast/leq/ [1997].
    • Keast, P.1
  • 102
    • 0017974820 scopus 로고
    • Midpoint difference method for analyzing beam structures
    • Beaufait FW, Reddien GW. Midpoint difference method for analyzing beam structures. Computers and Structures 1978; 8:745-751.
    • (1978) Computers and Structures , vol.8 , pp. 745-751
    • Beaufait, F.W.1    Reddien, G.W.2
  • 103
    • 0012031277 scopus 로고
    • A note on partial pivoting and Gaussian elimination
    • van Veldhuizen M. A note on partial pivoting and Gaussian elimination. Numerische Mathematik 1977; 29:1-10.
    • (1977) Numerische Mathematik , vol.29 , pp. 1-10
    • Van Veldhuizen, M.1
  • 104
    • 85037488470 scopus 로고    scopus 로고
    • Code lampak.f [1997]
    • Keast P, Fairweather G. Code lampak.f is available http://www.mscs.dal.ca/~keast/leq/ [1997].
    • Keast, P.1    Fairweather, G.2
  • 105
    • 0038048650 scopus 로고
    • Solving almost block diagonal linear equations on the CDC Cyber 205
    • Department of Mathematics, University of Manchester
    • Hay RI, Gladwell I. Solving almost block diagonal linear equations on the CDC Cyber 205. Numerical Analysis Report 98, Department of Mathematics, University of Manchester, 1987.
    • (1987) Numerical Analysis Report 98
    • Hay, R.I.1    Gladwell, I.2
  • 106
    • 85037487654 scopus 로고
    • Algorithms for the solution of linear systems arising from monomial spline basis functions
    • Dalhousie University, Computer Science Division
    • Majaess F, Keast P. Algorithms for the solution of linear systems arising from monomial spline basis functions. Dalhousie University, Computer Science Division, Technical Report 1987CS-11, 1987.
    • (1987) Technical Report 1987CS-11
    • Majaess, F.1    Keast, P.2
  • 107
    • 0005747440 scopus 로고
    • Packages for solving almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
    • Mason JC, Cox MG (eds). Chapman & Hall, London
    • Majaess F, Keast P, Fairweather G. Packages for solving almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. In Scientific Software Systems, Mason JC, Cox MG (eds). Chapman & Hall, London, 1990; 47-58.
    • (1990) Scientific Software Systems , pp. 47-58
    • Majaess, F.1    Keast, P.2    Fairweather, G.3
  • 108
    • 0026875275 scopus 로고
    • The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
    • Majaess F, Keast P, Fairweather G. The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. ACM Transactions on Mathematical Software 1992; 18:193-204.
    • (1992) ACM Transactions on Mathematical Software , vol.18 , pp. 193-204
    • Majaess, F.1    Keast, P.2    Fairweather, G.3
  • 109
    • 0026870307 scopus 로고
    • Algorithm 704: ABDPACK and ABBPACK, Fortran programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
    • Revised code abdpack.f available by anonymous ftp from directory /keast/abd_solvers at ftp.cs.dal.ca, solves a wider range of problems than the published ABDPACK
    • Majaess F, Keast P, Fairweather G, Bennett KR. Algorithm 704: ABDPACK and ABBPACK, Fortran programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions. ACM Transactions on Mathematical Software 1992; 18:205-210. Revised code abdpack.f available by anonymous ftp from directory /keast/abd_solvers at ftp.cs.dal.ca, solves a wider range of problems than the published ABDPACK.
    • (1992) ACM Transactions on Mathematical Software , vol.18 , pp. 205-210
    • Majaess, F.1    Keast, P.2    Fairweather, G.3    Bennett, K.R.4
  • 111
    • 84966203179 scopus 로고
    • A computational study of finite element methods for second order linear two-point boundary value problems
    • Keast P, Fairweather G, Diaz JC. A computational study of finite element methods for second order linear two-point boundary value problems. Mathematics of Computation 1983; 40:499-518.
    • (1983) Mathematics of Computation , vol.40 , pp. 499-518
    • Keast, P.1    Fairweather, G.2    Diaz, J.C.3
  • 112
    • 0442309280 scopus 로고
    • -1-Galerkin methods
    • Department of Computer Science, University of Toronto, Code rowcol.f is available by anonymous ftp from directory /keast/abd_solvers at ftp.cs.dal.ca
    • -1-Galerkin methods. Technical Report 158/82, Department of Computer Science, University of Toronto, 1982. Code rowcol.f is available by anonymous ftp from directory /keast/abd_solvers at ftp.cs.dal.ca.
    • (1982) Technical Report 158/82
    • Fairweather, G.1    Keast, P.2
  • 113
    • 28144454990 scopus 로고
    • An automatic continuation strategy for the solution of singularly perturbed linear boundary value problems
    • Code colmod available from library ode on netlib
    • Cash JR, Moore G, Wright RW. An automatic continuation strategy for the solution of singularly perturbed linear boundary value problems. Journal of Computational Physics 1995; 122:266-279. Code colmod available from library ode on netlib.
    • (1995) Journal of Computational Physics , vol.122 , pp. 266-279
    • Cash, J.R.1    Moore, G.2    Wright, R.W.3
  • 114
    • 0009284588 scopus 로고
    • Mesh selection for stiff two-point boundary value problems
    • Wright RW, Cash J, Moore G. Mesh selection for stiff two-point boundary value problems. Numerical Algorithms 1994; 7:205-224.
    • (1994) Numerical Algorithms , vol.7 , pp. 205-224
    • Wright, R.W.1    Cash, J.2    Moore, G.3
  • 117
    • 0018517232 scopus 로고
    • Algorithm 540. PDECOL: General collocation software for partial differential equations
    • Madsen NK, Sincovec RF. Algorithm 540. PDECOL: general collocation software for partial differential equations. ACM Transactions on Mathematical Software 1979; 5:326-351.
    • (1979) ACM Transactions on Mathematical Software , vol.5 , pp. 326-351
    • Madsen, N.K.1    Sincovec, R.F.2
  • 119
    • 0005729074 scopus 로고    scopus 로고
    • A method of lines package, based on monomial spline collocation, for systems of one dimensional parabolic equations
    • Griffiths DF, Watson GA (eds). World Scientific, Singapore
    • Nokonechny TB, Keast P, Muir PH. A method of lines package, based on monomial spline collocation, for systems of one dimensional parabolic equations. In Numerical Analysis, A.R. Mitchell 75th Birthday Volume, Griffiths DF, Watson GA (eds). World Scientific, Singapore, 1996;207-223.
    • (1996) Numerical Analysis, A.R. Mitchell 75th Birthday Volume , pp. 207-223
    • Nokonechny, T.B.1    Keast, P.2    Muir, P.H.3
  • 120
    • 0012033691 scopus 로고
    • A collection of problems for which Gaussian elimination with partial pivoting is unstable
    • Wright SJ. A collection of problems for which Gaussian elimination with partial pivoting is unstable. SIAM Journal on Scientific and Statistical Computing 1993; 14:231-238.
    • (1993) SIAM Journal on Scientific and Statistical Computing , vol.14 , pp. 231-238
    • Wright, S.J.1
  • 121
    • 21344482160 scopus 로고
    • Stable parallel elimination for boundary value ODE's
    • Wright SJ. Stable parallel elimination for boundary value ODE's. Numerische Mathematik 1994; 67:521-536.
    • (1994) Numerische Mathematik , vol.67 , pp. 521-536
    • Wright, S.J.1
  • 123
    • 0042470959 scopus 로고
    • Mixed block elimination for linear systems with wider borders
    • Code bemw is available from library linalg on netlib
    • Govaerts W, Pryce JD. Mixed block elimination for linear systems with wider borders. IMA Journal of Numerical Analysis 1993; 13:161-180. Code bemw is available from library linalg on netlib.
    • (1993) IMA Journal of Numerical Analysis , vol.13 , pp. 161-180
    • Govaerts, W.1    Pryce, J.D.2
  • 125
    • 0033245797 scopus 로고    scopus 로고
    • Stability and performance analysis of a block elimination solver for bordered linear systems
    • Yalamov PY, Paprzycki M. Stability and performance analysis of a block elimination solver for bordered linear systems. IMA Journal of Numerical Analysis 1999; 19:335-348.
    • (1999) IMA Journal of Numerical Analysis , vol.19 , pp. 335-348
    • Yalamov, P.Y.1    Paprzycki, M.2
  • 126
    • 0027702693 scopus 로고
    • A parallel version of the cyclic reduction algorithm on a hypercube
    • Amodio P, Mastronardi N. A parallel version of the cyclic reduction algorithm on a hypercube. Parallel Computing 1993; 19:1273-1281.
    • (1993) Parallel Computing , vol.19 , pp. 1273-1281
    • Amodio, P.1    Mastronardi, N.2
  • 127
    • 0038048652 scopus 로고
    • The parallel solution of ABD systems arising in numerical methods for BVPs for ODEs
    • Department of Computer Science, University of Toronto
    • Jackson KR, Pancer RN. The parallel solution of ABD systems arising in numerical methods for BVPs for ODEs. Technical Report 255/91, Department of Computer Science, University of Toronto, 1991.
    • (1991) Technical Report 255/91
    • Jackson, K.R.1    Pancer, R.N.2
  • 128
    • 0027911857 scopus 로고
    • Parallel treatment of block-bidiagonal matrices in the solution of ordinary differential boundary value problems
    • Wright K. Parallel treatment of block-bidiagonal matrices in the solution of ordinary differential boundary value problems. Journal of Computational and Applied Mathematics 1993; 45:191-200.
    • (1993) Journal of Computational and Applied Mathematics , vol.45 , pp. 191-200
    • Wright, K.1
  • 129
    • 0038387017 scopus 로고
    • On parallel methods for boundary value ODEs
    • Ascher UM, Chan SYP. On parallel methods for boundary value ODEs. Computing 1991; 46:1-17.
    • (1991) Computing , vol.46 , pp. 1-17
    • Ascher, U.M.1    Chan, S.Y.P.2
  • 130
    • 0030621835 scopus 로고    scopus 로고
    • A cyclic reduction approach to the numerical solution of boundary value ODEs
    • Amodio P, Paprzycki M. A cyclic reduction approach to the numerical solution of boundary value ODEs. SIAM Journal on Scientific Computing 1997; 18:56-68.
    • (1997) SIAM Journal on Scientific Computing , vol.18 , pp. 56-68
    • Amodio, P.1    Paprzycki, M.2
  • 132
    • 0039970386 scopus 로고    scopus 로고
    • Stable, parallel solution methods for tridiagonal systems of linear equations
    • May RL, EastonAK (eds). World Scientific, Singapore
    • Dun C, Hegland M, Osborne MR. Stable, parallel solution methods for tridiagonal systems of linear equations. In Computational Techniques & Applications: CTAC95, May RL, EastonAK (eds). World Scientific, Singapore, 1996; 267-274.
    • (1996) Computational Techniques & Applications: CTAC95 , pp. 267-274
    • Dun, C.1    Hegland, M.2    Osborne, M.R.3
  • 133
    • 0032386286 scopus 로고    scopus 로고
    • Wrap-around partitioning for block-bidiagonal linear systems
    • Hegland M, Osborne MR. Wrap-around partitioning for block-bidiagonal linear systems. IMA Journal of Numerical Analysis 1998; 18:373-384.
    • (1998) IMA Journal of Numerical Analysis , vol.18 , pp. 373-384
    • Hegland, M.1    Osborne, M.R.2
  • 134
    • 21344461874 scopus 로고    scopus 로고
    • Cost of stable algorithms for bordered almost block diagonal systems
    • Proceedings of ICIAM'95 - Numerical Analysis, Scientific Computation and Computer Science, Alefeld G, Mahrenholtz O, Mennicken R. (eds)
    • Kraut GL, Gladwell I. Cost of stable algorithms for bordered almost block diagonal systems. In Proceedings of ICIAM'95 - Numerical Analysis, Scientific Computation and Computer Science, Alefeld G, Mahrenholtz O, Mennicken R. (eds). Zeitschrift fur Angewandte Mathematik und Mechanik 1996; 76:151-154.
    • (1996) Zeitschrift fur Angewandte Mathematik und Mechanik , vol.76 , pp. 151-154
    • Kraut, G.L.1    Gladwell, I.2
  • 135
    • 3042985310 scopus 로고    scopus 로고
    • Parallel solution of almost block diagonal systems on a hypercube
    • Amodio P, Paprzycki M. Parallel solution of almost block diagonal systems on a hypercube. Linear Algebra and its Applications 1996; 241-243:85-103.
    • (1996) Linear Algebra and Its Applications , vol.241-243 , pp. 85-103
    • Amodio, P.1    Paprzycki, M.2
  • 136
    • 0026173680 scopus 로고
    • Solving almost block diagonal systems on parallel computers
    • Paprzycki M, Gladwell I. Solving almost block diagonal systems on parallel computers. Parallel Computing 1991; 17:133-153.
    • (1991) Parallel Computing , vol.17 , pp. 133-153
    • Paprzycki, M.1    Gladwell, I.2
  • 143
    • 0002540389 scopus 로고
    • A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations
    • Bunch JR, Rose DJ (eds). Academic Press: New York
    • Concus P, Golub GH, O'Leary DP. A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations. In Sparse Matrix Computations, Bunch JR, Rose DJ (eds). Academic Press: New York, 1976; 309-332.
    • (1976) Sparse Matrix Computations , pp. 309-332
    • Concus, P.1    Golub, G.H.2    O'Leary, D.P.3
  • 145
    • 0344780086 scopus 로고
    • An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
    • RIACS, NASA Ames Research Center, Moffett Field, The code qmrpack is available in directory qmr in library linalg of netlib
    • Freund RW, Gutknecht M, Nachtigal NM. An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. Technical Report 91.09, RIACS, NASA Ames Research Center, Moffett Field, 1991. The code qmrpack is available in directory qmr in library linalg of netlib.
    • (1991) Technical Report 91.09
    • Freund, R.W.1    Gutknecht, M.2    Nachtigal, N.M.3
  • 146
    • 3042882332 scopus 로고    scopus 로고
    • On the parallel solution of almost block diagonal systems
    • Amodio P, Paprzycki M. On the parallel solution of almost block diagonal systems. Control & Cybernetics 1996; 25:645-656.
    • (1996) Control & Cybernetics , vol.25 , pp. 645-656
    • Amodio, P.1    Paprzycki, M.2
  • 147
    • 0037710892 scopus 로고    scopus 로고
    • The parallel solution of almost block diagonal systems arising in numerical methods for BVPs in ODEs
    • Berlin
    • Pancer RN, Jackson KR. The parallel solution of almost block diagonal systems arising in numerical methods for BVPs in ODEs. In Proceedings of the 15th IMACS World Congress, vol. 2. Berlin, 1997; 57-62.
    • (1997) Proceedings of the 15th IMACS World Congress , vol.2 , pp. 57-62
    • Pancer, R.N.1    Jackson, K.R.2
  • 148
    • 21444452395 scopus 로고    scopus 로고
    • Recent advances in the parallel solution to almost block diagonal systems
    • Proceedings of ICIAM '95 - Applied Analysis, vol. 2, Mahrenholtz O, Mennicken R (eds).
    • Amodio P, Paprzycki M. Recent advances in the parallel solution to almost block diagonal systems. In Proceedings of ICIAM '95 - Applied Analysis, vol. 2, Mahrenholtz O, Mennicken R (eds). Zeitschrift fur Angewandte Mathematik und Mechanik 1996; 76:1-4.
    • (1996) Zeitschrift fur Angewandte Mathematik und Mechanik , vol.76 , pp. 1-4
    • Amodio, P.1    Paprzycki, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.