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- 1
-
E. L. Allgower.
Criteria for positive definiteness of some band matrices.
Numerische Mathematik, 16:157-162, 1970.
76
- 2
-
E. L. Allgower.
Exact inverse of certain band matrices.
Numerische Mathematik, 21:279-284, 1973.
74, 76
- 3
-
E. Asplund.
Inverses of matrices
which satisfy
for
.
Mathematica Scandinavica, 7:57-60, 1959.
11, 73
- 4
-
S. O. Asplund.
Finite boundary value problems solved by Green's matrix.
Mathematica Scandinavica, 7:49-56, 1959.
73
- 5
-
R. Baltzer.
Theorie und Anwendung der Determinanten.
S. Hirzel, fifth edition, 1881.
57
- 6
-
J. Baranger and M. Duc-Jacquet.
Matrices tridiagonales symmetriques et matrices factorisables.
Revue Française d'Informatique et de Recherche
Operationelle, 5(R-3):61-66, 1971.
75
- 7
-
W. W. Barrett.
A theorem on inverse of tridiagonal matrices.
Linear Algebra and Its Applications, 27:211-217, 1979.
9, 11, 77
- 8
-
W. W. Barrett and P. J. Feinsilver.
Gaussian families and a theorem on patterned matrices.
Journal of Applied Probability, 15:514-522, 1978.
64, 77
- 9
-
W. W. Barrett and P. J. Feinsilver.
Inverses of banded matrices.
Linear Algebra and Its Applications, 41:111-130, 1981.
5, 9, 11, 77, 213, 216
- 10
-
L. Berg.
Auflösung von gleichungssystemen mit einer bandmatrix.
Zeitschrift für Angewandte Mathematik und Mechanik,
57:373-380, 1977.
76
- 11
-
W. J. Berger and E. Saibel.
On the inversion of continuant matrices.
Journal of the Franklin Institute, 6:249-253, 1953.
73
- 12
-
R. Bevilacqua.
Structural and computational properties of band matrices.
appeared in R. Bevilacqua et al., Complexity of structured
computational problems, Applied mathematics monographs, CNR, giardini editori
e stanpatori, Pisa, pages 131-188, 1991.
72
- 13
-
R. Bevilacqua and M. Capovani.
Proprietà delle matrici tridiagonali ad elementi ed a blocchi.
Monografie dell'I.E.I., 1972.
72
- 14
-
R. Bevilacqua and M. Capovani.
Proprietà delle matrici a banda ad elementi ed a blocchi.
Bolletino Unione Matematica Italiana, 5(13-B):844-861, 1976.
76
- 15
-
R. Bevilacqua, B. Codenotti, and F. Romani.
Parallel solution of block tridiagonal linear systems.
Linear Algebra and Its Applications, 104:39-57, 1988.
79
- 16
-
R. Bevilacqua and G. M. Del Corso.
Existence, uniqueness and algorithms for matrix unitary reduction to
semiseparable form.
Tech. Report TR-03-12, University of Pisa, July 2003.
82, 153, 158
- 17
-
R. Bevilacqua, G. Lotti, and F. Romani.
Storage compression of inverses of band matrices.
Computers & Mathematics with Applications, 20(8):1-11, 1990.
79
- 18
-
R. Bevilacqua, F. Romani, and G. Lotti.
Parallel inversion of band matrices.
Computers and Artificial Intelligence, 9(5):493-501, 1990.
79
- 19
-
D. Bini, L. Gemignani, and V. Pan.
-like algorithms for generalized semiseparable matrices.
Tech. Report 1470, Department of Mathematics, University of Pisa,
2004.
30, 40, 42, 82, 143, 162, 213
- 20
-
C. F. Borges and W. B. Gragg.
A parallel divide and conquer algorithm for the generalized real
symmetric definite tridiagonal eigenproblem.
Numerical Linear Algebra (Kent, OH, 1992), pages 11-29, 1993.
de Gruyter, Berlin.
214
- 21
-
S. Börm, L. Grasedyck, and W. Hackbusch.
Introduction to hierarchical matrices with applications.
Technical Report 18, Max-Planck-Institut, Leipzig, 2002.
82, 215
- 22
-
M. Braun, S. A. Sofianos, D. G. Papageorgiou, and I. E. Lagaris.
An efficient Chebyshev Lanczos method for obtaining
eigensolutions of the Schrödinger equation on a grid.
Journal of Computational Physics, 126(2):315-327, 1996.
110
- 23
-
R. A. Brualdi and J. J. Q. Massey.
More on structure-ranks of matrices.
Linear Algebra and Its Applications, 183:193-199, 1993.
80
- 24
-
B. Bukhberger and G. A. Emel'yanenko.
Methods of inverting tridiagonal matrices.
Computational Mathematics and Mathematical Physics (translated
from Zhurnal Vychislitel'noi Matematiki i Matematicheskoi
Fiziki), 13:10-20, 1973.
75
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-
A. Bultheel, A. Cuyt, W. Van Assche, M. Van Barel, and B. Verdonk.
Generalizations of orthogonal polynomials.
TW report 375, Dept. Computer Science, 3001 Heverlee (Leuven),
December 2003.
70
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-
A. Bultheel, M. Van Barel, and P. Van Gucht.
Orthogonal basis functions in discrete least-squares rational
approximation.
Journal of Computational and Applied Mathematics,
164-165:175-194, 2004.
70
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-
R. L. Burden and J. D. Faires.
Numerical analysis.
PWS-Kent publishing company, fourth edition, 1988.
69
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-
W. S. Burnside and A. W. Panton.
An introduction to determinants, chapter from The theory of
equations.
Hodges, Figgis, & Co. and Longmans, Green & Co., 1899.
57
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-
W. L. Cao and W. J. Stewart.
A note on inverses of Hessenberg-like matrices.
Linear Algebra and Its Applications, 76:233-240, 1986.
79
- 30
-
M. Capovani.
Sulla determinazione della inversa delle matrici tridiagonali e
tridiagonali a blocchi.
Calcolo, 7:295-303, 1970.
74
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-
M. Capovani.
Su alcune proprietà delle matrici tridiagonali e pentadiagonali.
Calcolo, 8:149-159, 1971.
75
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-
K. M. Chandan.
The inverse of a certain matrix with an application.
Annals of Mathematical Statistics, 38:1289-1292, 1967.
64, 74
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-
S. Chandrasekaran, P. Dewilde, M. Gu, T. Pals, X. Sun, A.-J. van der Veen, and
D. White.
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of equations and least squares problems.
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70, 82
- 34
-
S. Chandrasekaran, P. Dewilde, M. Gu, T. Pals, and A.-J. van der Veen.
Fast stable solver for sequentially semi-separable linear systems of
equations.
Lecture Notes in Computer Science, 2552:545-554, 2002.
41, 70, 82
- 35
-
S. Chandrasekaran and M. Gu.
Fast and stable eigendecomposition of symmetric banded plus
semi-separable matrices.
Linear Algebra and Its Applications, 313:107-114, 2000.
20, 80, 92, 216
- 36
-
S. Chandrasekaran and M. Gu.
A fast and stable solver for recursively semi-separable systems of
linear equations.
Contemporary Mathematics, 281:39-53, 2001.
70, 82, 216
- 37
-
S. Chandrasekaran and M. Gu.
Fast and stable algorithms for banded plus semiseparable systems of
linear equations.
SIAM Journal on Matrix Analysis and its Applications,
25(2):373-384, 2003.
81
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-
S. Chandrasekaran and M. Gu.
A divide and conquer algorithm for the eigendecomposition of
symmetric block-diagonal plus semi-separable matrices.
Numerische Mathematik, 96(4):723-731, February 2004.
81, 92, 216
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-
D. Colton and R. Kress.
Inverse acoustic and electromagnetic scattering theory.
Springer-Verlag, second edition, 1998.
82
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C. Corduneanu.
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Press Syndicate of the University of Cambridge, 1991.
69
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-
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Cambridge, University Press, 1913.
57
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-
J. K. Cullum and R. A. Willoughby.
Lanczos algorithms for large symmetric eigenvalue
computations.
Birkhäuser, Boston, 1985.
100
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-
S. Demko.
Inverses of band matrices and local convergence of spline
projections.
SIAM Journal on Numerical Analysis, 14(4):616-619, 1977.
76, 215
- 44
-
S. Demko, W. F. Moss, and P. W. Smith.
Decay rates for inverses of band matrices.
Mathematics of Computation, 43:491-499, 1984.
78, 215
- 45
-
J. W. Demmel.
Applied numerical linear algebra.
SIAM, 1997.
2, 100, 101
- 46
-
J. W. Demmel and W. Kahan.
Accurate singular values of bidiagonal matrices.
SIAM Journal on Scientific Computing, 11(5):873-912, 1990.
214
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-
J. W. Demmel and K. Veselic.
Jacobi's method is more accurate than
.
SIAM Journal on Matrix Analysis and its Applications,
13(4):1204-1245, 1992.
128, 203, 214
- 48
-
P. Dewilde and A.-J. van der Veen.
Time-varying systems and computations.
Kluwer academic publishers, Boston, June 1998.
41, 70, 82, 215
- 49
-
P. Dewilde and A.-J. van der Veen.
Inner-outer factorization and the inversion of locally finite systems
of equations.
Linear Algebra and Its Applications, 313:53-100, February
2000.
41, 82
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-
I. S. Dhillon.
A new
algorithm for the symmetric tridiagonal
eigenvalue/eigenvector problem.
PhD thesis, University of California, 1989.
214
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-
A. A. Dubrulle and G. H. Golub.
A multishift
iteration without computation of the shifts.
Numerical Algorithms, 7(2-4):173-181, 1994.
215
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-
Y. Eidelman.
Fast recursive algorithm for a class of structured matrices.
Applied Mathematical Letters, 13:57-62, 2000.
82
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-
Y. Eidelman and I. Gohberg.
Inversion formulas and linear complexity algorithm for diagonal plus
semiseparable matrices.
Computers & Mathematics with Applications, 33(4):69-79,
August 1996.
80
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-
Y. Eidelman and I. Gohberg.
Fast inversion algorithms for diagonal plus semiseparable matrices.
Integral Equations and Operator Theory, 27(2):165-183, 1997.
80
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-
Y. Eidelman and I. Gohberg.
A look ahead block schur algorithm for diagonal plus semiseparable
matrices.
Computers & Mathematics with Applications, 35(10):25-34,
1997.
80
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-
Y. Eidelman and I. Gohberg.
On a new class of structured matrices.
Integral Equations and Operator Theory, 34:293-324, 1999.
41, 70, 82
- 57
-
Y. Eidelman and I. Gohberg.
Algorithms for inversion of diagonal plus semiseparable operator
matrices.
Integral Equations and Operator Theory, 44(2):172-211, 2002.
82
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-
Y. Eidelman and I. Gohberg.
A modification of the Dewilde van der Veen method for inversion
of finite structured matrices.
Linear Algebra and Its Applications, 343-344:419-450, April
2002.
41, 82
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Y. Eidelman and I. Gohberg.
Fast inversion algorithms for a class of structured operator
matrices.
Linear Algebra and Its Applications, 371:153-190, 2003.
82
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Decay rates of inverses of banded
-matrices that are near to
Toeplitz matrices.
Linear Algebra and Its Applications, 109:247-277, 1988.
79
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Some observations on inverses of band matrices and low rank
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11, 80
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83
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Linear Algebra and Its Applications, 359:79-90, 2003.
15, 54
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Rational Krylov matrices and
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diagonal-plus-semiseparable matrices.
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82
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Structural and computational properties of possibly singular
semiseparable matrices.
Linear Algebra and its Applications, 340:183-198, 2001.
20, 81
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A Lanczos type algorithm for the
-factorization of regular
Cauchy matrices.
Numerical Linear Algebra with Applications, 9:305-319, 2002.
70
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Direct and inverse eigenvalue problems, for
diagonal-plus-semiseparable matrices.
Numerical Algorithms, 34:313-324, 2003.
70, 81
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Fast and stable algorithms for reducing diagonal plus semi separable
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Contemporary Mathematics, 323:105-118, 2003.
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Generalized band matrices and their inverses.
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79, 80
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Structure ranks of matrices.
Linear Algebra and Its Applications, 179:119-127, 1993.
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Linear Algebra and Its Applications, 373:143-151, 2003.
6, 11, 15, 29, 34, 37, 38, 82
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5, 6, 9, 11, 78, 216
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Linear Algebra and Its Applications, 85:49-56, 1987.
11, 12, 79, 216
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