[1] Allaire, G., and Kaber, S. M. 2008. Numerical linear algebra. New York: Springer. Translated from the 2002 French original by Karim Trabelsi.
[2] Arnoldi, W. E. 1951. The principle of minimized iteration in the solution of the matrix eigenvalue problem. Quart. Appl. Math., 9, 17–29.
[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.
[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.
[5] Axelsson, O. 1985. A survey of preconditioned iterative methods for linear systems of algebraic equations. BIT, 25(1), 166–187.
[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.
[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.
[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.
[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.
[12] Bebendorf, M. 2000. Approximation of boundary element matrices. Numer. Math., 86(4), 565–589.
[13] Bebendorf, M. 2008. Hierarchical matrices – A means to efficiently solve elliptic boundary value problems. Berlin: Springer.
[14] Bebendorf, M. 2011. Adaptive cross approximation of multivariate functions. Constr. Approx., 34(2), 149–179.
[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.
[16] Benzi, M. 2002. Preconditioning techniques for large linear systems: a survey. J. Comput. Phys., 182(2), 418–477.
[17] Benzi, M., and Tůma, M. 1999. A comparative study of sparse approximate inverse preconditioners. Appl. Numer. Math., 30(2–3), 305–340.
[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.
[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.
[20] Björck, A. 1996. Numerical methods for least squares problems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[21] Bjöorck, A. 2015. Numerical methods in matrix computations. Cham: Springer.
[22] Boyd, S., and Vandenberghe, L. 2004. Convex optimization. Cambridge: Cambridge University Press.
[23] Brandt, A. 1977. Multi-level adaptive solutions to boundary-value problems. Math. Comp., 31(138), 333–390.
[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.
[25] Brenner, S., and Scott, L. 1994. The Mathematical Theory of Finite Element Methods. 3rd edn. New York: Springer.
[26] Briggs, W., and McCormick, S. 1987. Introduction. Pages 1–30 of: Multigrid methods. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[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).
[28] Bruaset, A. M. 1995. A survey of preconditioned iterative methods. Harlow: Longman Scientific & Technical.
[29] Candès, E. J. 2006. Compressive sampling. Pages 1433–1452 of: International Congress of Mathematicians. Vol. III. Zürich: European Mathematical Society.
[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.
[31] Candès, E. J., and Tao, T. 2005. Decoding by linear programming. IEEE Trans. Inform. Theory, 51(12), 4203–4215.
[32] Candès, E. J., and Wakin, M. B. 2008. An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21–30.
[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.
[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.
[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.
[36] Chow, E., and Saad, Y. 1998. Approximate inverse preconditioners via sparse– sparse iterations. SIAM J. Sci. Comput., 19(3), 995–1023.
[37] Coppersmith, D., and Winograd, S. 1990. Matrix multiplication via arithmetic progressions. J. Symboli. Comput., 9(3), 251–280.
[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).
[40] Cullum, J. 1996. Iterative methods for solving Ax = b, GMRES/FOM versus QMR/BiCG. Adv. Comput. Math., 6(1), 1–24.
[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.
[43] de Berg, M., van Kreveld, M., Overmars, M., and Schwarzkopf, O. 1997. Computational Geometry. Berlin: Springer.
[44] Demmel, J. W. 1997. Applied numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[45] DeVore, R. A. 2007. Deterministic constructions of compressed sensing matrices. J. Complexity, 23(4–6), 918–925.
[46] Donoho, D. L. 2006. Compressed sensing. IEEE Trans. Inform. Theory, 52(4), 1289–1306.
[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.
[48] Escalante, R., and Raydan, M. 2011. Alternating projection methods. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[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.
[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.
[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.
[52] Ford, W. 2015. Numerical linear algebra with applications. Amsterdam: Elsevier/ Academic Press.
[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.
[54] Foucart, S., and Rauhut, H. 2013. A mathematical introduction to compressive sensing. New York: Birkhäuser/Springer.
[55] Fox, L. 1964. An introduction to numerical linear algebra. Oxford: Clarendon Press.
[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.
[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.
[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.
[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.
[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.
[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.
[65] Golub, G. H., and Reinsch, C. 1970. Singular value decomposition and least squares solutions. Numer. Math., 14(5), 403–420.
[66] Golub, G. H., and Van Loan, C. F. 2013. Matrix computations. 4th edn. Baltimore, MD: Johns Hopkins University Press.
[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.
[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.
[69] Greenbaum, A. 1997. Iterative methods for solving linear systems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[70] Griebel, M. 1994. Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen. Stuttgart: B. G. Teubner.
[71] Griebel, M., and Oswald, P. 1995. On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math., 70(2), 163–180.
[72] Grote, M. J., and Huckle, T. 1997. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput., 18(3), 838–853.
[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.
[74] Hackbusch, W. 1985. Multi-grid methods and applications. Berlin: Springer.
[75] Hackbusch, W. 1994. Iterative solution of large sparse systems of equations. New York: Springer. Translated and revised from the 1991 German original.
[76] Hackbusch, W. 1999. A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matrices. Computing, 62(2), 89–108.
[77] Hackbusch, W. 2015. Hierarchical matrices: algorithms and analysis. Heidelberg: Springer.
[78] Hackbusch, W., and Börm, S. 2002. Data-sparse approximation by adaptive H2- matrices. Computing., 69(1), 1–35.
[79] Hackbusch, W., Grasedyck, L., and Börm, S. 2002. An introduction to hierarchical matrices. Mathematic. Bohemica, 127(2), 229–241.
[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.
[81] Hansen, P. C. 1992. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev., 34(4), 561–580.
[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.
[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).
[84] Higham, N. J. 1990. Exploiting fast matrix multiplication within the level 3 BLAS. ACM Trans. Math. Software, 16(4), 352–368.
[85] Higham, N. J. 2002. Accuracy and stability of numerical algorithms. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[86] Householder, A. S. 1958. Unitary triangularization of a nonsymmetric matrix. J. Assoc. Comput. Mach., 5, 339–342.
[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.
[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.
[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.
[90] Lanczos, C. 1952. Solution of systems of linear equations by minimizediterations. J. Research Nat. Bur. Standards, 49, 33–53.
[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.
[92] Liesen, J., and Strakoš, Z. 2013. Krylov subspace methods – Principles and analysis. Oxford: Oxford University Press.
[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.
[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.
[95] Meister, A. 1999. Numerik linearer Gleichungssysteme – Eine Einführung in moderne Verfahren. Braunschweig: Friedrich Vieweg & Sohn.
[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.
[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.
[98] Ostrowski, A. M. 1959. A quantitative formulation of Sylvester's law of inertia. Proc. Nat. Acad. Sci. U.S.A., 45, 740–744.
[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.
[100] Parlett, B. N. 1998. The symmetric eigenvalue problem. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). Corrected reprint of the 1980 original.
[101] Pearcy, C. 1966. An elementary proof of the power inequality for the numerical radius. Michigan Math. J., 13, 289–291.
[102] Quarteroni, A., and Valli, A. 1999. Domain decomposition methods for partial differential equations. New York: Clarendon Press.
[103] Saad, Y. 1994. Highly parallel preconditioners for general sparse matrices. Pages 165–199 of: Recent advances in iterative methods. New York: Springer.
[104] Saad, Y. 2003. Iterative methods for sparse linear systems. 2nd edn. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[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.
[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.
[107] Schaback, R., and Wendland, H. 2005. Numerische Mathematik. 5th edn. Berlin: Springer.
[108] Schatzman, M. 2002. Numerical Analysis: A Mathematical Introduction. Oxford: Oxford University Press.
[109] Simoncini, V., and Szyld, D. B. 2002. Flexible inner–outer Krylov subspace methods. SIAM J. Numer. Anal., 40(6), 2219–2239.
[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.
[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.
[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.
[114] Sonneveld, P. 1989. CGS, a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 10(1), 36–52.
[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.
[116] Steinbach, O. 2005. Lösungsverfahren für lineare Gleichungssysteme. Wiesbaden: Teubner.
[117] Stewart, G. W. 1998. Matrix algorithms. Volume I: Basic decompositions. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[118] Stewart, G.W. 2001. Matrix algorithms. Volume II: Eigensystems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[119] Stewart, G. W., and Sun, J. G. 1990. Matrix perturbation theory. Boston, MA: Academic Press.
[120] Strassen, V. 1969. Gaussian elimination is not optimal. Numer. Math., 13, 354–356.
[121] Süli, E., and Mayers, D. F. 2003. An introduction to numerical analysis. Cambridge: Cambridge University Press.
[122] Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B, 58(1), 267–288.
[123] Toselli, A., and Widlund, O. 2005. Domain decomposition methods – algorithms and theory. Berlin: Springer.
[124] Trefethen, L. N., and Bau, III, D. 1997. Numerical linear algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
[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.
[126] Van de Velde, E. F. 1994. Concurrent scientific computing. New York: Springer.
[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.
[128] van der Vorst, H. A. 2009. Iterative Krylov methods for large linear systems. Cambridge: Cambridge University Press. Reprint of the 2003 original.
[129] Varga, R. S. 2000. Matrix iterative analysis. Expanded edn. Berlin: Springer.
[130] Wathen, A. 2007. Preconditioning and convergence in the right norm. Int. J. Comput. Math., 84(8), 1199–1209.
[131] Wathen, A. J. 2015. Preconditioning. Acta Numer., 24, 329–376.
[132] Watkins, D. S. 2010. Fundamentals of matrix computations. 3rd edn. Hoboken, NJ: John Wiley & Sons.
[133] Wendland, H. 2005. Scattered data approximation. Cambridge: Cambridge University Press.
[134] Werner, J. 1992a. Numerische Mathematik. Band 1: Lineare und nichtlineare Gleichungssysteme, Interpolation, numerische Integration. Braunschweig: Friedrich Vieweg & Sohn.
[135] Werner, J. 1992b. Numerische Mathematik. Band 2: Eigenwertaufgaben, lineare Optimierungsaufgaben, unrestringierte Optimierungsaufgaben. Braunschweig: Friedrich Vieweg & Sohn.
[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.
[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.
[139] Young, D. M. 1970. Convergence properties of the symmetric and unsymmetric successive overrelaxation methods and related methods. Math. Comp., 24, 793–807.
[140] Young, D. M. 1971. Iterative Solution of Large Linear Systems. New York: Academic Press.
