Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-13T03:25:15.193Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  20 November 2017

Holger Wendland
Affiliation:
Universität Bayreuth, Germany
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Numerical Linear Algebra
An Introduction
, pp. 395 - 402
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Allaire, G., and Kaber, S. M. 2008. Numerical linear algebra. New York: Springer. Translated from the 2002 French original by Karim Trabelsi.CrossRefGoogle Scholar
[2] Arnoldi, W. E. 1951. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math., 9, 17–29.CrossRefGoogle Scholar
[3] Arya, S., and Mount, D. M. 1993. Approximate nearest neighbor searching. Pages 271–280 of: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms. New York: ACM Press.Google Scholar
[4] Arya, S., and Mount, D.M. 1995. Approximate range searching. Pages 172–181 of: Proceedings of the 11th Annual ACM Symposium on Computational Geometry. New York: ACM Press.Google Scholar
[5] Axelsson, O. 1985. A survey of preconditioned iterative methods for linear systems of algebraic equations. BIT, 25(1), 166–187.CrossRefGoogle Scholar
[6] Axelsson, O. 1994. Iterative solution methods. Cambridge: Cambridge University Press.
[7] Axelsson, O., and Barker, V. A. 1984. Finite element solution of boundary value problems. Orlando FL: Academic Press.
[8] Axelsson, O., and Lindskog, G. 1986. On the rate of convergence of the preconditioned conjugate gradient method. Numer. Math., 48(5), 499–523.Google Scholar
[9] Bandeira, A. S., Fickus, M., Mixon, D. G., and Wong, P. 2013. The road to deterministic matrices with the restricted isometry property. J. Fourier Anal. Appl., 19(6), 1123–1149.CrossRefGoogle Scholar
[10] Baraniuk, R., Davenport, M., DeVore, R., and Wakin, M. 2008. A simple proof of the restricted isometry property for random matrices. Constr. Approx., 28(3), 253–263.CrossRefGoogle Scholar
[11] Beatson, R. K., and Greengard, L. 1997. A short course on fast multipole methods. Pages 1–37 of: Ainsworth, M., Levesley, J., Light, W., and Marletta, M. (eds.), Wavelets, multilevel methods and elliptic PDEs. 7th EPSRC numerical analysis summer school, University of Leicester, Leicester, GB, July 8–19, 1996. Oxford: Clarendon Press.Google Scholar
[12] Bebendorf, M. 2000. Approximation of boundary element matrices. Numer. Math., 86(4), 565–589.CrossRefGoogle Scholar
[13] Bebendorf, M. 2008. Hierarchical matrices – A means to efficiently solve elliptic boundary value problems. Berlin: Springer.Google Scholar
[14] Bebendorf, M. 2011. Adaptive cross approximation of multivariate functions. Constr. Approx., 34(2), 149–179.Google Scholar
[15] Bebendorf, M., Maday, Y., and Stamm, B. 2014. Comparison of some reduced representation approximations. Pages 67–100 of: Reduced order methods for modeling and computational reduction. Cham: Springer.Google Scholar
[16] Benzi, M. 2002. Preconditioning techniques for large linear systems: a survey. J. Comput. Phys., 182(2), 418–477.CrossRefGoogle Scholar
[17] Benzi, M., and Tůma, M. 1999. A comparative study of sparse approximate inverse preconditioners. Appl. Numer. Math., 30(2–3), 305–340.CrossRefGoogle Scholar
[18] Benzi, M., Cullum, J. K., and Tůma, M. 2000. Robust approximate inverse preconditioning for the conjugate gradient method. SIAM J. Sci.Comput., 22(4), 1318–1332.CrossRefGoogle Scholar
[19] Benzi, M., Meyer, C. D., and Tůma, M. 1996. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput., 17(5), 1135–1149.CrossRefGoogle Scholar
[20] Björck, A. 1996. Numerical methods for least squares problems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[21] Bjöorck, A. 2015. Numerical methods in matrix computations. Cham: Springer.CrossRefGoogle Scholar
[22] Boyd, S., and Vandenberghe, L. 2004. Convex optimization. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[23] Brandt, A. 1977. Multi-level adaptive solutions to boundary-value problems. Math. Comp., 31(138), 333–390.CrossRefGoogle Scholar
[24] Brandt, A., McCormick, S., and Ruge, J. 1985. Algebraic multigrid (AMG) for sparse matrix equations. Pages 257–284 of: Sparsity and its applications (Loughborough, 1983). Cambridge: Cambridge University Press.Google Scholar
[25] Brenner, S., and Scott, L. 1994. The Mathematical Theory of Finite Element Methods. 3rd edn. New York: Springer.CrossRefGoogle Scholar
[26] Briggs, W., and McCormick, S. 1987. Introduction. Pages 1–30 of: Multigrid methods. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).Google Scholar
[27] Briggs, W. L., Henson, V. E., and McCormick, S. F. 2000. A multigrid tutorial. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[28] Bruaset, A. M. 1995. A survey of preconditioned iterative methods. Harlow: Longman Scientific & Technical.Google Scholar
[29] Candès, E. J. 2006. Compressive sampling. Pages 1433–1452 of: International Congress of Mathematicians. Vol. III. Zürich: European Mathematical Society.Google Scholar
[30] Candès, E. J. 2008. The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris, 346(9–10), 589–592.CrossRefGoogle Scholar
[31] Candès, E. J., and Tao, T. 2005. Decoding by linear programming. IEEE Trans. Inform. Theory, 51(12), 4203–4215.Google Scholar
[32] Candès, E. J., and Wakin, M. B. 2008. An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.CrossRefGoogle Scholar
[33] Candès, E. J., Romberg, J. K., and Tao, T. 2006. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math., 59(8), 1207–1223.CrossRefGoogle Scholar
[34] Chan, T. F., Gallopoulos, E., Simoncini, V., Szeto, T., and Tong, C. H. 1994. A quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric systems. SIAM J. Sci. Comput., 15(2), 338–347.CrossRefGoogle Scholar
[35] Cherrie, J. B., Beatson, R. K., and Newsam, G. N. 2002. Fast evaluation of radial basis functions: Methods for generalised multiquadrics in Rn. SIAM J. Sci. Comput., 23, 1272–1310.CrossRefGoogle Scholar
[36] Chow, E., and Saad, Y. 1998. Approximate inverse preconditioners via sparse– sparse iterations. SIAM J. Sci. Comput., 19(3), 995–1023.CrossRefGoogle Scholar
[37] Coppersmith, D., and Winograd, S. 1990. Matrix multiplication via arithmetic progressions. J. Symboli. Comput., 9(3), 251–280.CrossRefGoogle Scholar
[38] Cosgrove, J. D. F., Díaz, J. C., and Griewank, A. 1992. Approximate inverse preconditionings for sparse linear systems. International Journal of Computer Mathematics, 44(1–4), 91–110.
[39] Cosgrove, J. D. F., Díaz, J. C., and Macedo, Jr., C. G. 1991. Approximate inverse preconditioning for nonsymmetric sparse systems. Pages 101–111 of: Advances in numerical partial differential equations and optimization (Mérida, 1989). Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).Google Scholar
[40] Cullum, J. 1996. Iterative methods for solving Ax = b, GMRES/FOM versus QMR/BiCG. Adv. Comput. Math., 6(1), 1–24.CrossRefGoogle Scholar
[41] Datta, B. N. 2010. Numerical linear algebra and applications. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[42] Davenport, M. A., Duarte, M. F., Eldar, Y. C., and Kutyniok, G. 2012. Introduction to compressed sensing. Pages 1–64 of: Compressed sensing. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[43] de Berg, M., van Kreveld, M., Overmars, M., and Schwarzkopf, O. 1997. Computational Geometry. Berlin: Springer.CrossRefGoogle Scholar
[44] Demmel, J. W. 1997. Applied numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[45] DeVore, R. A. 2007. Deterministic constructions of compressed sensing matrices. J. Complexity, 23(4–6), 918–925.CrossRefGoogle Scholar
[46] Donoho, D. L. 2006. Compressed sensing. IEEE Trans. Inform. Theory, 52(4), 1289–1306.Google Scholar
[47] Elman, H. C., Silvester, D. J., and Wathen, A. J. 2014. Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. 2nd edn. Oxford: Oxford University Press.CrossRefGoogle Scholar
[48] Escalante, R., and Raydan, M. 2011. Alternating projection methods. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[49] Faber, V., and Manteuffel, T. 1984. Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM J. Numer. Anal., 21(2), 352–362.CrossRefGoogle Scholar
[50] Fischer, B. 2011. Polynomial based iteration methods for symmetric linear systems. Philadelphia, PA: Society for Industrial and AppliedMathematics (SIAM). Reprint of the 1996 original.CrossRefGoogle Scholar
[51] Fletcher, R. 1976. Conjugate gradient methods for indefinite systems. Pages 73–89 of: Numerical analysis (Proceedings of the 6th Biennial Dundee Conference, University of Dundee, Dundee, 1975). Berlin: Springer.Google Scholar
[52] Ford, W. 2015. Numerical linear algebra with applications. Amsterdam: Elsevier/ Academic Press.Google Scholar
[53] Fornasier, M., and Rauhut, H. 2011. Compressive sensing. Pages 187–228 of: Scherzer, O. (ed.), Handbook of Mathematical Methods in Imaging. New York: Springer.Google Scholar
[54] Foucart, S., and Rauhut, H. 2013. A mathematical introduction to compressive sensing. New York: Birkhäuser/Springer.CrossRefGoogle Scholar
[55] Fox, L. 1964. An introduction to numerical linear algebra. Oxford: Clarendon Press.Google Scholar
[56] Francis, J. G. F. 1961/1962a. The QR transformation: a unitary analogue to the LR transformation. I. Comput. J., 4, 265–271.
[57] Francis, J. G. F. 1961/1962b. The QR transformation. II. Comput. J., 4, 332–345.
[58] Freund, R. W. 1992. Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J. Sci. Statist. Comput., 13(1), 425–448.CrossRefGoogle Scholar
[59] Freund, R.W. 1993. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput., 14(2), 470–482.CrossRefGoogle Scholar
[60] Freund, R. W., and Nachtigal, N. M. 1991. QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer. Math., 60(3), 315–339.CrossRefGoogle Scholar
[61] Freund, R.W., Gutknecht, M. H., and Nachtigal, N. M. 1993. An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. SIAM J. Sci. Comput., 14(1), 137–158.CrossRefGoogle Scholar
[62] Gasch, J., and Maligranda, L. 1994. On vector-valued inequalities of the Marcinkiewicz–Zygmund, Herz and Krivine type. Math. Nachr., 167, 95–129.
[63] Goldberg, M., and Tadmor, E. 1982. On the numerical radius and its applications. Linear Algebra Appl., 42, 263–284.CrossRefGoogle Scholar
[64] Golub, G., and Kahan, W. 1965. Calculating the singular values and pseudoinverse of a matrix. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2, 205–224.CrossRefGoogle Scholar
[65] Golub, G. H., and Reinsch, C. 1970. Singular value decomposition and least squares solutions. Numer. Math., 14(5), 403–420.Google Scholar
[66] Golub, G. H., and Van Loan, C. F. 2013. Matrix computations. 4th edn. Baltimore, MD: Johns Hopkins University Press.Google Scholar
[67] Golub, G. H., Heath, M., and Wahba, G. 1979. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21(2), 215–223.CrossRefGoogle Scholar
[68] Gould, N. I. M., and Scott, J. A. 1998. Sparse approximate-inverse preconditioners using norm-minimization techniques. SIAM J. Sci. Comput., 19(2), 605–625.CrossRefGoogle Scholar
[69] Greenbaum, A. 1997. Iterative methods for solving linear systems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[70] Griebel, M. 1994. Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen. Stuttgart: B. G. Teubner.CrossRefGoogle Scholar
[71] Griebel, M., and Oswald, P. 1995. On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math., 70(2), 163–180.CrossRefGoogle Scholar
[72] Grote, M. J., and Huckle, T. 1997. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput., 18(3), 838–853.CrossRefGoogle Scholar
[73] Gutknecht, M. H. 2007. A brief introduction to Krylov space methods for solving linear systems. Pages 53–62 of: Kaneda, Y., Kawamura, H., and Sasai, M. (eds.), Frontiers of Computational Science. Berlin: Springer.Google Scholar
[74] Hackbusch, W. 1985. Multi-grid methods and applications. Berlin: Springer.CrossRefGoogle Scholar
[75] Hackbusch, W. 1994. Iterative solution of large sparse systems of equations. New York: Springer. Translated and revised from the 1991 German original.CrossRefGoogle Scholar
[76] Hackbusch, W. 1999. A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices. Computing, 62(2), 89–108.CrossRefGoogle Scholar
[77] Hackbusch, W. 2015. Hierarchical matrices: algorithms and analysis. Heidelberg: Springer.CrossRefGoogle Scholar
[78] Hackbusch, W., and Börm, S. 2002. Data-sparse approximation by adaptive H2- matrices. Computing., 69(1), 1–35.CrossRefGoogle Scholar
[79] Hackbusch, W., Grasedyck, L., and Börm, S. 2002. An introduction to hierarchical matrices. Mathematic. Bohemica, 127(2), 229–241.Google Scholar
[80] Hackbusch, W., Khoromskij, B., and Sauter, S. A. 2000. On H2-matrices. Pages 9–29 of: Lectures on applied mathematics (Munich, 1999). Berlin: Springer.Google Scholar
[81] Hansen, P. C. 1992. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev., 34(4), 561–580.CrossRefGoogle Scholar
[82] Henrici, P. 1958. On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices. J. Soc. Indust. Appl. Math., 6, 144–162.CrossRefGoogle Scholar
[83] Hestenes, M. R., and Stiefel, E. 1952. Methods of conjugate gradients for solving linear systems. J. Research Nat. Bur. Standards, 49, 409–436 (1953).CrossRefGoogle Scholar
[84] Higham, N. J. 1990. Exploiting fast matrix multiplication within the level 3 BLAS. ACM Trans. Math. Software, 16(4), 352–368.CrossRefGoogle Scholar
[85] Higham, N. J. 2002. Accuracy and stability of numerical algorithms. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[86] Householder, A. S. 1958. Unitary triangularization of a nonsymmetric matrix. J. Assoc. Comput. Mach., 5, 339–342.CrossRefGoogle Scholar
[87] Kolotilina, L. Y., and Yeremin, A. Y. 1993. Factorized sparse approximate inverse preconditionings. I. Theory. SIAM J. Matrix Anal. Appl., 14(1), 45–58.CrossRefGoogle Scholar
[88] Krasny, R., and Wang, L. 2011. Fast evaluation of multiquadric RBF sums by a Cartesian treecode. SIAM J. Sci. Comput., 33(5), 2341–2355.Google Scholar
[89] Lanczos, C. 1950. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Research Nat. Bur. Standards, 45, 255–282.CrossRefGoogle Scholar
[90] Lanczos, C. 1952. Solution of systems of linear equations by minimizediterations. J. Research Nat. Bur. Standards, 49, 33–53.CrossRefGoogle Scholar
[91] Le Gia, Q. T., and Tran, T. 2010. An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical basis functions. Journal of Complexity, 26, 552–573.CrossRefGoogle Scholar
[92] Liesen, J., and Strakoš, Z. 2013. Krylov subspace methods – Principles and analysis. Oxford: Oxford University Press.Google Scholar
[93] Maligranda, L. 1997. On the norms of operators in the real and the complex case. Pages 67–71 of: Proceedings of the Second Seminar on Banach Spaces and Related Topics. Kitakyushu: Kyushu Institute of Technology.Google Scholar
[94] Meijerink, J. A., and van der Vorst, H. A. 1977. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comp., 31(137), 148–162.Google Scholar
[95] Meister, A. 1999. Numerik linearer Gleichungssysteme – Eine Einführung in moderne Verfahren. Braunschweig: Friedrich Vieweg & Sohn.CrossRefGoogle Scholar
[96] Meister, A., and Vömel, C. 2001. Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws. Adv. Comput. Math., 14(1), 49–73.CrossRefGoogle Scholar
[97] Morozov, V. A. 1984. Methods for solving incorrectly posed problems. New York: Springer. Translated from the Russian by A. B. Aries, Translation edited by Z. Nashed.CrossRefGoogle Scholar
[98] Ostrowski, A. M. 1959. A quantitative formulation of Sylvester's law of inertia. Proc. Nat. Acad. Sci. U.S.A., 45, 740–744.CrossRefGoogle Scholar
[99] Paige, C. C., and Saunders, M. A. 1975. Solutions of sparse indefinite systems of linear equations. SIAM J. Numer. Anal., 12(4), 617–629.CrossRefGoogle Scholar
[100] Parlett, B. N. 1998. The symmetric eigenvalue problem. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). Corrected reprint of the 1980 original.CrossRefGoogle Scholar
[101] Pearcy, C. 1966. An elementary proof of the power inequality for the numerical radius. Michigan Math. J., 13, 289–291.Google Scholar
[102] Quarteroni, A., and Valli, A. 1999. Domain decomposition methods for partial differential equations. New York: Clarendon Press.Google Scholar
[103] Saad, Y. 1994. Highly parallel preconditioners for general sparse matrices. Pages 165–199 of: Recent advances in iterative methods. New York: Springer.Google Scholar
[104] Saad, Y. 2003. Iterative methods for sparse linear systems. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[105] Saad, Y., and Schultz, M. H. 1986. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 7(3), 856–869.CrossRefGoogle Scholar
[106] Saad, Y., and van der Vorst, H. A. 2000. Iterative solution of linear systems in the 20th century. J. Comput. Appl. Math., 123(1-2), 1–33.CrossRefGoogle Scholar
[107] Schaback, R., and Wendland, H. 2005. Numerische Mathematik. 5th edn. Berlin: Springer.Google Scholar
[108] Schatzman, M. 2002. Numerical Analysis: A Mathematical Introduction. Oxford: Oxford University Press.Google Scholar
[109] Simoncini, V., and Szyld, D. B. 2002. Flexible inner–outer Krylov subspace methods. SIAM J. Numer. Anal., 40(6), 2219–2239.Google Scholar
[110] Simoncini, V., and Szyld, D. B. 2005. On the occurrence of superlinear convergence of exact and inexact Krylov subspace methods. SIAM Rev., 47(2), 247–272.CrossRefGoogle Scholar
[111] Simoncini, V., and Szyld, D. B. 2007. Recent computational developments in Krylov subspace methods for linear systems. Numer. Linear Algebr. Appl., 14(1), 1–59.Google Scholar
[112] Sleijpen, G. L. G., and Fokkema, D. R. 1993. BiCGstab(l) for linear equations involving unsymmetric matrices with complex spectrum. Electron. Trans. Numer. Anal., 1(Sept.), 11–32 (electronic only).
[113] Smith, K. T., Solmon, D. C., and Wagner, S. L. 1977. Practical and mathematical aspects of the problem of reconstructing objects from radiographs. Bull. Amer. Math. Soc., 83, 1227–1270.CrossRefGoogle Scholar
[114] Sonneveld, P. 1989. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 10(1), 36–52.CrossRefGoogle Scholar
[115] Sonneveld, P., and van Gijzen, M. B. 2008/09. IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations. SIAM J. Sci. Comput., 31(2), 1035–1062.Google Scholar
[116] Steinbach, O. 2005. Lösungsverfahren für lineare Gleichungssysteme. Wiesbaden: Teubner.CrossRefGoogle Scholar
[117] Stewart, G. W. 1998. Matrix algorithms. Volume I: Basic decompositions. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[118] Stewart, G.W. 2001. Matrix algorithms. Volume II: Eigensystems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[119] Stewart, G. W., and Sun, J. G. 1990. Matrix perturbation theory. Boston, MA: Academic Press.Google Scholar
[120] Strassen, V. 1969. Gaussian elimination is not optimal. Numer. Math., 13, 354–356.CrossRefGoogle Scholar
[121] Süli, E., and Mayers, D. F. 2003. An introduction to numerical analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[122] Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B, 58(1), 267–288.Google Scholar
[123] Toselli, A., and Widlund, O. 2005. Domain decomposition methods – algorithms and theory. Berlin: Springer.CrossRefGoogle Scholar
[124] Trefethen, L. N., and Bau, III, D. 1997. Numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).CrossRefGoogle Scholar
[125] Trottenberg, U., Oosterlee, C. W., and Schüller, A. 2001. Multigrid. San Diego, CA: Academic Press. With contributions by A. Brandt P., Oswald and K. Stüben.Google Scholar
[126] Van de Velde, E. F. 1994. Concurrent scientific computing. New York: Springer.CrossRefGoogle Scholar
[127] van der Vorst, H. A. 1992. Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 13(2), 631–644.CrossRefGoogle Scholar
[128] van der Vorst, H. A. 2009. Iterative Krylov methods for large linear systems. Cambridge: Cambridge University Press. Reprint of the 2003 original.Google Scholar
[129] Varga, R. S. 2000. Matrix iterative analysis. Expanded edn. Berlin: Springer.CrossRefGoogle Scholar
[130] Wathen, A. 2007. Preconditioning and convergence in the right norm. Int. J. Comput. Math., 84(8), 1199–1209.CrossRefGoogle Scholar
[131] Wathen, A. J. 2015. Preconditioning. Acta Numer., 24, 329–376.CrossRefGoogle Scholar
[132] Watkins, D. S. 2010. Fundamentals of matrix computations. 3rd edn. Hoboken, NJ: John Wiley & Sons.Google Scholar
[133] Wendland, H. 2005. Scattered data approximation. Cambridge: Cambridge University Press.Google Scholar
[134] Werner, J. 1992a. Numerische Mathematik. Band 1: Lineare und nichtlineare Gleichungssysteme, Interpolation, numerische Integration. Braunschweig: Friedrich Vieweg & Sohn.Google Scholar
[135] Werner, J. 1992b. Numerische Mathematik. Band 2: Eigenwertaufgaben, lineare Optimierungsaufgaben, unrestringierte Optimierungsaufgaben. Braunschweig: Friedrich Vieweg & Sohn.Google Scholar
[136] Wimmer, H. K. 1983. On Ostrowski's generalization of Sylvester's law of inertia. Linear Algebra Appl., 52/53, 739–741.
[137] Xu, J. 1992. Iterative methods by space decomposition and subspace correction. SIAM Rev., 34(4), 581–613.CrossRefGoogle Scholar
[138] Yin, W., Osher, S., Goldfarb, D., and Darbon, J. 2008. Bregman iterative algorithms for l1-minimization with applications to compressed sensing. SIAM J. Imagin. Sci., 1(1), 143–168.CrossRefGoogle Scholar
[139] Young, D. M. 1970. Convergence properties of the symmetric and unsymmetric successive overrelaxation methods and related methods. Math. Comp., 24, 793–807.CrossRefGoogle Scholar
[140] Young, D. M. 1971. Iterative Solution of Large Linear Systems. New York: Academic Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bibliography
  • Holger Wendland, Universität Bayreuth, Germany
  • Book: Numerical Linear Algebra
  • Online publication: 20 November 2017
  • Chapter DOI: https://doi.org/10.1017/9781316544938.011
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bibliography
  • Holger Wendland, Universität Bayreuth, Germany
  • Book: Numerical Linear Algebra
  • Online publication: 20 November 2017
  • Chapter DOI: https://doi.org/10.1017/9781316544938.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • Holger Wendland, Universität Bayreuth, Germany
  • Book: Numerical Linear Algebra
  • Online publication: 20 November 2017
  • Chapter DOI: https://doi.org/10.1017/9781316544938.011
Available formats
×