algebra.bib

@article{runge,
 author={Runge, C.},
 title={Ueber die numerische {A}ufl\"osung von {D}ifferentialgleichungen},
 journal={Math. Ann.},
 volume={46},
 number={2},
 pages={167-178},
 year={1895},
 doi={10.1007/BF01446807},
}

@book{wedderburn,
author={Wedderburn, J. H. M},
title={Lectures on matrices},
series={Colloquim publications},
volume={17},
year={1934},
publisher={AMS},
address={New York}
}

@article{dirac,
author={Dirac, P. A. M.},
title={A new notation for quantum mechanics},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
volume={35},
number={3},
pages={416-418},
year={1939},
doi={10.1017/S0305004100021162}
}

@book{hardy-1949,
 author={Hardy, G. H.},
 title={Divergent series},
 year={1949},
 publisher={Clarendon Press},
 address={Oxford},
}

@article{kantorovich-1948,
 author={Kantorovich, L. V.},
 title={Funktsionallniy analyz i prikladnaya matematika},
 journal={Uspehi Mat. Nauk},
 volume={3},
 number={28},
 pages={89-185},
 year={1945}
}

@article{kantorovich-1948rus,
 author={Канторович, Л. В.},
 title={Функциональный анализ и прикладная математика},
 journal={УМН},
 volume={3},
 number={28},
 pages={89-185},
 year={1948},
 url={http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=8775&what=fullt&option_lang=rus},
}

@techreport{woodbury-1950,
  author={Woodbury, Max A},
  title={Inverting modified matrices},
  type={Statistical Research Group, Memo. Rep.},
  number={42},
  institution={Princeton University},
  address={Princeton, N. J},
  year={1950},
}

@article{shermanmorrison-1950,
 author={Sherman, Jack and Morrison, Winifred J.},
 title={Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix},
 journal={Ann. Math. Statist.},
 volume={21},
 number={1},
 pages={124-127},
 year={1950},
 doi={10.1214/aoms/1177729893}
}

@article{hager-1989,
 author={Hager, William W},
 title={Updating the inverse of a matrix},
 journal={{SIAM} Rev.},
 volume={31},
 number={2},
 pages={221-239},
 year={1989},
 doi={10.1137/1031049}
}

@article{schechter-1959,
 title={On the inversion of certain matrices},
 author={Schechter, S.},
 journal={Mathematical Tables and Other Aids to Computation},
 volume={66},
 number={13},
 pages={73-77},
 year={1959}
}

@book{gantmacher-1959,
 title={The theory of matrices},
 author={Gantmacher, F. R.},
 year={1959},
 publisher={Clelsea},
 address={NY}
}

@article{householder-1960,
 author={Bauer, F. L. and Householder, A. S.},
 title={Some inequalities involving the euclidian condition of a matrix},
 journal={Numerische Mathematik},
 volume={2},
 number={1},
 pages={308-311},
 year={1960},
 doi={10.1007/BF01386231}
}

@article{kantorovich-1961,
 title={Two remarks on the {Kantorovich} inequality},
 author={Henrici, P.},
 journal={The Americal Mathematical Monthly},
 volume={68},
 number={9},
 year={1961},
 pages={904-906}
}

@article{kingman-1961,
 title={A convexity property of positive matrices},
 author={Kingman, J. F. C.},
 journal={Quart. J. Math. Oxford},
 volume={12},
 pages={283-284},
 year={1961},
 doi={10.1093/qmath/12.1.283}
}

@article{wilkinson-1961,
 title={Error analysis of direct method of matrix inversion},
 author={Wilkinson, J. H.},
 journal={J Assoc. Comput. Machinery},
 volume={8},
 year={1961},
 pages={281-330},
 doi={10.1145/321075.321076}
}

@article{golubkahan-1965,
  title={Calculating the singular values and pseudo-inverse of a matrix},
  author={Golub, G. and Kahan, W.},
  journal={SIAM J. Numer. Anal.},
  volume={2},
  number={2},
  pages={205--224},
  year={1965},
  publisher={SIAM}
}

@article{mueller-1966,
  title={{Householder's method for complex matrices and eigensystems of hermitian matrices}},
  author={Mueller, D.J.},
  journal={Numerische Mathematik},
  volume={8},
  number={1},
  pages={72--92},
  year={1966},
}

@article{strang-split-1968,
     title = {On the Construction and Comparison of Difference Schemes},
     author = {Strang, Gilbert},
     journal = {SIAM Journal on Numerical Analysis},
     volume = {5},
     number = {3},
     pages = {506-517},
     url = {http://www.jstor.org/stable/2949700},
     year = {1968},
}

@article{hastings-mcmc-1970,
 title={Monte {Carlo} sampling methods using {Markov} chains and their applications},
 author={Hastings, W. K.},
 journal={Biometrika},
 volume={57},
 number={1},
 pages={97-109},
 year={1970},
 doi={10.1093/biomet/57.1.97}
}

@article{paige-1976,
  title={Error analysis of the {Lanczos} algorithm for tridiagonalizing a symmetric matrix},
  author={Paige, C. C.},
  journal={IMA J. Appl. Math.},
  volume={18},
  number={3},
  pages={341},
  year={1976}
}

@article{stewart-1977,
 title={On the perturbation of pseudo--inverses, projections and linear least squares problems},
 author={Stewart, G. W.},
 journal={SIAM Review},
 volume={19},
 number={4},
 pages={634-662},
 year={1977},
 doi={10.1137/1019104}
}

@article{bartholdi-1982,
    title={A good submatrix is hard to find},
    author={Bartholdi III, John J},
    journal={Operations Research Lett.},
    volume={1},
    number={5},
    pages={190--193},
    year={1982},
}

@article{donoho-1989,
      title={Uncertainty principle and signal recovery},
      author={Donoho, David L. and Stark, Philip B.},
      journal={SIAM J. Appl. Math.},
      volume={49},
      number={3},
      pages={906-931},
      year={1989},
      doi={10.1137/0149053}
}

@article{kantorovich-1990,
 title={Matrix version of the {Cauchy} and {Kantorovich} inequalities},
 author={Marshall, A. W. and Olkin, L.},
 journal={Aequationes Mathematicae},
 volume={40},
 pages={89-93},
 year={1990}
}

@article{poole-1992,
 title={A geometric analysis of {Gaussian} elimination. {II}},
 author={Neal, Larry and Poole, George},
 journal={Linear Alg. Appl.},
 volume={173},
 pages={239-264},
 year={1992},
 doi={10.1016/0024-3795(92)90432-A}
}

@article{knuth-1985,
 title={Semi--optimal bases for linear dependencies},
 author={Knuth, Donald E.},
 journal={Linear and Multilinear Algebra},
 volume={17},
 pages={1-4},
 year={1985},
 doi={10.1080/03081088508817636}
 }

@article{foster-1997,
 title={The growth factor and efficiency of {Gaussian} elimination with rook pivoting},
 author={Foster, Leslie V.},
 journal={J. Comput. Appl. Math.},
 volume={86},
 number={1},
 pages={177-194},
 year={1997},
 doi={10.1016/S0377-0427(97)00154-4}
}

@article{poole-2000,
  title={The Rook's pivoting strategy},
  author={Poole, George and Neal, Larry},
  journal={J. Comput. Appl. Math.},
  volume={123}, 
  issue={1–2},
  year={2000}, 
  pages={353-369},
  doi={10.1016/S0377-0427(00)00406-4},
}

@book{defant-1993,
  title={Tensor norms and operator ideals},
  author={Defant, A. and Floret, K.},
  year={1993},
  publisher={North-Holland, Amsterdam}
}


@article{gu-rrqr-1995,
  title={Efficient algorithms for computing a strong rank--revealing {QR} factorization},
  author={Gu, Ming and Eisenstat, C.},
  journal={SIAM J. Sci. Comput.}, 
  volume={17},
  number={4}, 
  pages={848-869},
  year={1996},
  doi={10.1137/0917055},
}

@article{chu-rank1-1995,
title={A rank-one reduction formula and its applications to matrix factorizations},
author={Chu, Moody T. and Funderlic, Robert E. and Golub, Gene H.},
journal={SIAM Review},
volume={37},
number={4},
pages={512-530},
year={1995}
}

@article{marchuk-split-1995,
author={Marchuk, G. I.},
title={Splitting-up methods for non-stationary problems},
journal={Comput. Math. Math. Phys. (in russian)},
year={1995},
volume={35},
number={6},
pages={843--849},
}

@article{marchuk-split-1995rus,
author={Марчук, Г. И.},
title={Методы расщепления для решения нестационарных задач},
journal={Ж. вычисл. матем. и матем. физ.},
year={1995},
volume={35},
number={6},
pages={843--849},
language={russian},
url={http://www.mathnet.ru/php/getFT.phtml?jrnid=zvmmf&paperid=2383&what=fullt&option_lang=rus},
}

@book{golub-1996,
 title={Matrix computations},
 author={Golub, G.H. and Van Loan, C.F.},
 year={1996},
 publisher={Johns Hopkins University Press, Baltimore, MD}
}
@book{golub-2013,
 title={Matrix Computations},
 author={Golub, G. H. and Van Loan, C. F.},
 year={2013},
 publisher={Johns Hopkins University Press, Baltimore, MD}
}

@book{greenbaum-1997,
  title={Iterative methods for solving linear systems},
  author={Greenbaum, A.},
  year={1997},
  publisher={SIAM, Philadephia}
}

@book{demmel,
 title={Applied numerical linear algebra},
 author={Demmel, J. W.},
 year={1997},
 publisher={Society for Industrial Mathematics}
}

@article{Hackbusch-H-1999,
author="Hackbusch, W.",
title="A Sparse Matrix Arithmetic Based on $\mathcal{H}$-Matrices. {P}art {I}: {I}ntroduction to $\mathcal{H}$-Matrices",
journal="Computing",
year="1999",
volume="62",
number="2",
pages="89--108",
doi="10.1007/s006070050015",
}

@Article{Eidelman-qsep-1999,
author="Eidelman, Y. and Gohberg, I.",
title="On a new class of structured matrices",
journal="Integral Equations and Operator Theory",
year="1999",
volume="34",
number="3",
pages="293--324",
doi="10.1007/BF01300581",
}

@book{trefethen-spectral-2000,
	title={Spectral methods in MATLAB},
	author={Trefethen, L. N.},
	publisher={SIAM},
	address={Philadelphia},
	year={2000}
}

@article{pan-rrlu-2000,
  title={On the existence and computation of rank--revealing {LU} factorizations},
  author={Pan, C.-T.},
  journal={Linear Algebra Appl.},
  volume={316},
  number={1-3},
  pages={199-222},
  year={2000},
  doi={10.1016/S0024-3795(00)00120-8},
}



@article{elad-2002,
      title={A generalized uncertainty principle and sparse representation in pairs of bases},
      author={Elad, Michael and Bruckstein, Alfred M.},
      journal={IEEE Trans. Inform. Theory},
      volume={48},
      number={9},
      pages={2558-2567},
      year={2002},
      doi={10.1109/TIT.2002.801410}
}


@article{randomrank-2007,
      title={The rank of a random matrix},
      author={Feng, X. and Zhang, Z.},
      journal={Appl. Math. and Comp.},
      volume={185},
      number={3},
      pages={689-694},
      year={2007},
      publisher={Elseiver},
      doi={10.1016/j.amc.2006.07.076}
}

@book{bogachev-2007,
 author={Bogachev, Vladimir I.},
 title={Measure theory},
 publisher={Springer-Verlag},
 address={Berlin Heidelberg},
 year={2007}
}

@book{hornjohnson-1985,
author = {Horn, R. A. and Johnson, C.R.},
title = {Matrix analysis},
publisher = {Cambridge university press},
year = {1985},
}
@article{demanet-randskel-2013,
    title={Sublinear randomized algorithms for skeleton decompositions},
    author={Chiu, Jiawei and Demanet, Laurent},
    journal={SIAM J. Matrix Anal. Appl.},
    volume={34},
    year={2013},
    number={3},
    pages={1361--1383},
}
@article{boumal-manopt-2014,
    title={Manopt, a {MATLAB} toolbox for optimization on manifolds},
    author={Boumal, Nicolas and Mishra, Bamdev and Absil, Pierre-Antoine and Sepulchre, Rodolphe and others},
    journal={Journal of Machine Learning Research},
    volume={15},
    number={1},
    pages={1455--1459},
    year={2014}
}

@book{gvl-matcomp-2013,
  title={Matrix computations},
  author={Golub, Gene H. and Van Loan, Charles F.},
  edition = {4th},
  year={2013},
  publisher={JHU Press}
}

@book{tee-briefan-2012,
  title={A brief introduction to numerical analysis},
  author={Tyrtyshnikov, {E}ugene {E}},
  year={2012},
  publisher={{S}pringer {S}cience \& {B}usiness {M}edia}
}

@book{tref-nla-1997,
title={Numerical linear algebra},
author={Trefethen, Lloyd N and Bau III, David},
volume={50},
year={1997},
publisher={{SIAM}}
}

@article{dongarra-top10,
 title={Introduction to the top 10 algorithms},
 author={Dongarra, Jack and Sullivan, Francis},
 journal={Computing in Science \& Engineering},
 volume={2},
 number={1},
 pages={22-23},
 year={2000},
}

@article{stewart-lr-2000,
 title={The decompositional approach to matrix computation},
 author={Stewart, G. W.},
 journal={Computing in Science \& Engineering},
 volume={2},
 number={1},
 pages={50-59},
 year={2000},
 doi={10.1109/5992.814658}
}

@book{trefethen-approx-2013,
 author={Trefethen, Lloyd N.},
 title={Approximation Theory and Approximation Practice},
 year={2013},
 publisher={SIAM}
}

@article{trefethen-chebfun2-2013,
 title={An Extension of {Chebfun} to Two Dimensions},
 author={Townsend, Alex and Trefethen, Lloyd N.},
 journal={SIAM J. Sci. Comput.}, 
 volume={35},
 number={6}, 
 pages={C495-C518},
 year={2013},
 doi={10.1137/130908002}
}

@article{trefethen-chebfun3-2017,
 title={Chebfun in Three Dimensions},
 author={Hashemi, Behnam and Trefethen, Lloyd N.},
 journal={SIAM J. Sci. Comput.}, 
 volume={39},
 number={5}, 
 pages={C341-C363},
 year={2017},
 doi={10.1137/16M1083803}
}