Reports availble for downloading

Recent and future publications

D. Calvetti, R.K. Dash, M.E. Cabrera and E. Somersalo
Local regularization method applied to estimating oxygen consumption during muscle activities
Inverse Problems, to appear.
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D. Calvetti and E. Somersalo
Priorconditioners for linear systems
Inverse Problems, 21 (2005), pp. 1397-1418.
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D. Calvetti and E. Somersalo
Statistical elimination of boundary artifacts
Inverse Problems, 21 (2005), pp. 1697-1714.
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D. Calvetti, J. Kaipio and E. Somersalo
Aristotelian prior boundary conditions
Intl. J. Math. Comp. Sci., to appear.
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D. Calvetti
Preconditioned iterative methods for linear discrete ill-posed problems from a Bayesian inversion perspective
J.Comput. Appl. Math, to appear.
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D. Calvetti and E. Somersalo
Bayesian image deblurring and boundary effects
Advanced Signal Processing Algorithms, Architectures and Implementations XV, edited by F.T. Luk, Proc. of SPIE Vol. 5910 (SPIE, Bellingham, WA 2005), pp. 59100X-1-59100X-9. PDF file
D. Calvetti and E. Somersalo
Local regularization and Bayesian hypermodels
Advanced Signal Processing Algorithms, Architectures and Implementations XV, edited by F.T. Luk, Proc. of SPIE Vol. 5910 (SPIE, Bellingham, WA 2005), pp. 59100W-1-59100W-9.
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A.V. Chvetsov, D. Calvetti, J.W. Sohn and T.J. Kinsella
Regularization of inverse planning for intensity-modulated radiotherapy
Medical Physics 32, 501 (2005) and
Virtual Journal of Biological Physics Research (2005)

D. Calvetti and L. Reichel
Tikhonov regularization of large scale problems
BIT, 43 (2003), pp. 263-283.
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D. Calvetti, B. Lewis and L. Reichel.
A hybrid GMRES and TV-norm based method for image restoration
Advanced Signal Processing Algorithms, Architectures and Implementations XII, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 4791, The International Society for Optical Engineering, Bellingham, WA, 2002, pp. 192--200.
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D. Calvetti and L. Reichel
Gauss quadrature applied to trust region computations
Numer. Algorithms, 34 (2003), pp. 85-102.
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D. Calvetti and L. Reichel
Symmetric Gauss-Lobatto and modified anti-Gauss rules
BIT, 43 (2003), pp. 224-239.
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D. Calvetti, L. Reichel and F. Sgallari
A modified companion matrix based on Newton polynomials
in Fast Algorithms for Structured Matrices: Theory and Applications, ed. V. Olshevski, Contemporary Mathematics, vol 323, Amer. math. Soc., Providence, RI, 2003, pp. 179--186.
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D. Calvetti and L. Reichel
On the evaluation of polynomial coefficients
Numer. Algorithms, Numer. Algorithms, 33 (2003), pp. 153-161.
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J. Baglama, D. Calvetti and L. Reichel
irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix
ACM Trans. Math. Software, 29 (2203), pp. 337-348.
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D. Calvetti, S-M. Kim and L. Reichel
The restarted QR-algorithm for eigenvalue computation of structured matrices
J. Comput. Appl. Math., 149 (2002), pp.415--422.
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D. Calvetti, L. Reichel and A. Shuibi,
Enriched Krylov subspace methods for ill-posed problems
Linear Algebra Appl., 362 (2003), pp. 257-273.
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J. Baglama, D. Calvetti and L. Reichel,
IRBL: an implicitly restarted block-Lanczos method for large-scale Hermitian eigenproblems
SIAM J.Sci. Comput., 24 (2003), pp 1650-1677.
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D. Calvetti, B. Lewis and L. Reichel,
GMRES, L-curves and discrete ill-posed problems
BIT, 42 (2002), pp. 44-65.
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D. Calvetti, B. Lewis and L. Reichel,
On the regularizaing properties of the GMRES method
Numer. Math., 91 (2002), pp. 605-625.
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D. Calvetti, P.C. Hansen and L. Reichel,
L-curve curvature bounds via Lanczos bidiagonalization
Elec. Trans. Numer. Anal., 14(2002), pp. 134-149.
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D. Calvetti, L. Reichel and A. Shuibi,
L-curve and curvature bounds for Tikhonov regularization
Numer. Algorithms, to appear.
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D. Calvetti and L. Reichel,
Lanczos-based exponential filtering for discrete ill-posed problems
Numer. Algorithms, 29(2002), pp.134-149.
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D. Calvetti and L. Reichel,
Pole placement preconditioning
Linear Algebra Appl., 366 (2003), pp. 99-120.
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Selected paper and reports grouped by topic

Large Ill-Posed Problems, Applications to Image Restoration

D. Calvetti, L. Reichel, F. Sgallari and G. Spaletta.
An iterative method for image reconstruction from projections
Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, ed. J.G. Lewis, SIAM, Philadelphia, 1994, pp. 92--96.
D. Calvetti, L. Reichel, Q. Zhang.
Iterative solution methods for ill-posed problems
in Advanced Signal Processing Algorithms, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 2563, The International Society for Optical Engineering, Bellingham, WA, 1995, pp. 338--347.
D. Calvetti and L. Reichel.
Application of ADI iterative methods to the restoration of noisy images
SIAM J. Matrix Anal., 17 (1996), pp. 165--186.
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D. Calvetti, L. Reichel and Q. Zhang.
Iterative solution methods for ill-posed problems
12th Annual Review on Computational and Applied Electromagnetism, ACES, 1996, pp. 638--644.
D. Calvetti, N. Levenberg and L. Reichel.
Iterative methods for X-AXB=C
J. Comput. Appl. Math., 86 (1997), pp. 73--101.
D. Calvetti, B. Lewis and L. Reichel.
Smooth or abrupt: a comparison of regularization methods
Advanced Signal Processing Algorithms, Architectures and Implementations VIII, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 3461, The International Society for Optical Engineering, Bellingham, WA, 1998, pp. 286--295.
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D. Calvetti, L. Reichel and Q. Zhang.
Iterative solution methods for large linear discrete ill-posed problems
Applied and Computational Control, Signals and Circuits, 1 (1999), pp. 313--367.
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D. Calvetti, L. Reichel and Q. Zhang.
Iterative exponential filtering for large discrete ill-posed problems
Numer. Math., 83 (1999), pp. 535--556.
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D. Calvetti, G.H. Golub and L. Reichel.
Estimation of the L-curve via Lanczos bidiagonalization
BIT, 39 (1999), pp. 603--619.
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D. Calvetti, L. Reichel, F. Sgallari and G. Spaletta.
A regularizing Lanczos iteration method for underdetermined linear systems
J. Comput. Appl. Math., 115 (2000), pp. 101--120.
D. Calvetti, L. Reichel, F. Sgallari and G. Spaletta
Tikhonov regularization and the L-curve for large, discrete ill-posed problems
J. Comput. Appl. Math., 123 (2000), pp. 423--446.
D. Calvetti, S. Morigi L. Reichel and F. Sgallari.
An L-ribbon for large underdetermined linear discrete ill-posed problems
Numer. Algorithms, 25 (2000), pp. 89--107.
D. Calvetti, B. Lewis and L. Reichel
Restoration of images with spatially variant blur by the GMRES method
Advanced Signal Processing Algorithms, Architectures, and Implementations X, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 4116, The International Society for Optical Engineering, Bellingham, WA, 2000, pp. 364--374.
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D. Calvetti, B. Lewis and L. Reichel
An L-curve for the MINRES method
Advanced Signal Processing Algorithms, Architectures, and Implementations X, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 4116, The International Society for Optical Engineering, Bellingham, WA, 2000, pp. 385--395.
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D. Calvetti, B. Lewis and L. Reichel
On the choice of subspace for iterative methods for linear discrete ill-posed problems Int. J. Appl. Math. Comput. Sci., 11 (2001), to appear.
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D. Calvetti, B. Lewis and L. Reichel
GMRES, L-curves and discrete ill-posed problems
BIT, to appear.
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D. Calvetti, B. Lewis and L. Reichel
On the regularizing properties of the GMRES method
Numer. Math., to appear.
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D. Calvetti, P.C. Hansen and L. Reichel
L-curve curvature bounds via Lanczos bidiagonalization
Elec. Trans. Numer. Anal., 14 (2002), pp. 20--35.
D. Calvetti, B. Lewis and L. Reichel
Krylov subspace iterative methods for nonsymmetric discrete ill-posed problems in image restoration
Advanced Signal Processing Algorithms, Architectures, and Implementations X, ed. F.T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 4116, The International Society for Optical Engineering, Bellingham, WA, 2001, submitted.
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Large Eigenvalue Problems, Path Following and Liquid Crystal Modeling

D. Calvetti, L. Reichel and D.C. Sorensen
An implicitly restarted Lanczos method for large symmetric eigenvalue problems
Elec. Trans. Numer. Anal., 2 (1994), pp. 1--21.
J. Baglama, D. Calvetti and L. Reichel
Iterative methods for computing a few eigenvalues of a large symmetric matrix
BIT, 36 (1996), pp. 400--421.
J. Baglama, D. Calvetti, L. Reichel and A. Ruttan
Computation of a few close eigenvalues of a large matrix with application to liquid crystal modeling
J. Comput. Phys., 146 (1998), pp. 203--226.
J. Baglama, D. Calvetti and L. Reichel
Fast Leja points
Elec. Trans. Numer. Anal., 7 (1998), pp. 126--140.
D. Calvetti and L. Reichel
A block Lanczos method for large continuation problems
Numer. Algorithms, 21 (1999), pp. 109--118.
D. Calvetti and L. Reichel
Iterative methods for large continuation problems
J. Comput. Appl. Math., 123 (2000), pp. 217--240.

Iterative Solution of Linear Systems of Equations

D. Calvetti, L. Reichel and J. Petersen
A parallel implementation of the GMRES algorithm
Numerical Linear Algebra, eds. L. Reichel, A. Ruttan and R.S. Varga, de Gruyter, Berlin, 1993, pp. 31--46.
D. Calvetti, G.H. Golub and L. Reichel
Gaussian quadrature applied to adaptive Chebyshev iteration
Recent Advances in Iterative Methods, eds. G. Golub, A. Greenbaum and M. Luskin, Springer, New York, 1994, pp. 31--44.
D. Calvetti, G.H. Golub and L. Reichel
An adaptive Chebyshev iterative method for nonsymmetric linear systems based on modified moments
Numer. Math., 67 (1994), pp. 21--40.
D. Calvetti and L. Reichel
Application of a block modified Chebyshev algorithm to the iterative solution of symmetric linear systems with multiple right hand side vectors
Numer. Math., 68 (1994), pp. 3--16.
D. Calvetti, L. Reichel and Q. Zhang
An adaptive semiiterative method for symmetric semidefinite linear systems
Approximation and Computation, ed. R.V.M. Zahar, Int'l Series of Numer. Math. \# 119, Birkh\"auser, Basel, 1994, pp. 77--96.
D. Calvetti, L. Reichel and Q. Zhang
Conjugate gradient algorithms for symmetric inconsistent linear systems
Proceedings of the Cornelius Lanczos International Centenary Conference, eds. J.D. Brown, M.T. Chu, D.C. Ellison and R.J. Plemmons, SIAM, Philadelphia, 1994, pp. 267--272.
D. Calvetti and L. Reichel
Adaptive Richardson iteration based on Leja points
J. Comput. Appl. Math., 71 (1996), pp. 267--286.
D. Calvetti and L. Reichel
A hybrid method for symmetric positive definite linear systems
Numer. Algorithms, 11 (1996), pp. 79--98.
D. Calvetti and L. Reichel
An adaptive Richardson iteration method for indefinite linear systems
Numer. Algorithms, 12 (1996), pp. 125--149.
D. Calvetti and L. Reichel
A hybrid iterative method for symmetric indefinite linear systems
J. Comput. Appl. Math., 92 (1998), pp. 109--133.
J. Baglama, D. Calvetti, G.H. Golub and L. Reichel
Adaptively preconditioned GMRES algorithms
SIAM J. Sci. Comput., 20 (1999), pp. 243--269.
D. Calvetti, B. Lewis and L. Reichel
GMRES-type methods for inconsistent systems
Linear Algebra Appl., 316 (2000), pp. 157--169.
D. Calvetti, S. Morigi, L. Reichel and F. Sgallari
An iterative method with error estimators
J. Comput. Appl. Math., 127 (2001), pp. 93--119.
D. Calvetti, S. Morigi, L. Reichel and F. Sgallari
Computable error bounds and estimates for the conjugate gradient method
Numer. Algorithms., 25 (2000), pp. 79--88.

Orthogonal Polynomials and Quadrature

G.S. Ammar, D. Calvetti and L. Reichel
Continuation methods for the computation of zeros of Szego polynomials
Linear Algebra Appl., 249 (1996), pp. 125--155.
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D. Calvetti, L. Reichel and F. Sgallari
Application of anti-Gauss quadrature rules in linear algebra
Applications and Computation of Orthogonal Polynomials, eds. W. Gautschi, G.H. Golub and G. Opfer, Birkhauser, Basel, 1999, pp. 41--56.
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D. Calvetti, G.H. Golub and L. Reichel
A computable error bound for matrix functionals
J. Comput. Appl. Math., 103 (1999), pp. 301--306.
G.S. Ammar, D. Calvetti and L. Reichel
Computation of Gauss-Kronrod quadrature rules with non-positive weights
Elec. Trans. Numer. Anal., 9 (1999), pp. 26--38.
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D. Calvetti, G.H. Golub, W.B. Gragg and L. Reichel
Computation of Gauss-Kronrod quadrature rules
Math. Comp., 69 (2000), pp. 1035--1052.
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Structured Problems in Linear Algebra, Applications to Signal Processing and Control Theory

D. Calvetti and L. Reichel
A Chebyshev-Vandermonde solver
Linear Algebra Appl., 172 (1992), pp. 219--229.
D. Calvetti and L. Reichel
Fast inversion of Vandermonde-like matrices involving orthogonal polynomials
BIT, 33 (1993), pp. 473--484.
G.S. Ammar, D. Calvetti and L. Reichel
Computing the poles of autoregressive models from the reflection coefficients
Proceedings of the Thirty-First Annual Allerton Conference on Communication, Control and Computing, University of Illinois at Urbana-Champaign Press, Urbana-Champaign, 1994, pp. 247--254.
D. Calvetti and L. Reichel
On the solution of Cauchy systems of equations
Elec. Trans. Numer. Anal., 4 (1996), pp. 125--136.
D. Calvetti and L. Reichel
Factorizations of Cauchy matrices
J. Comput. Appl. Math., 86 (1997), pp. 103--123.
D. Calvetti and L. Reichel
Numerical aspects of some solution methods for large Sylvester-observer equations
Proceedings of the 36th IEEE Conference on Decision and Control, IEEE, Piscataway, 1997, pp. 4389--4393.
D. Calvetti, B. Lewis and L. Reichel
On the solution of the single input pole placement problem
Mathematical Theory of Networks and Systems, eds. A. Beghi, L. Finesso and G. Picci, Il Poliografo, Padova, 1998, pp. 585--588.
D. Calvetti and L. Reichel
On an inverse eigenvalue problem for Jacobi matrices
Adv. Comput. Math., 11 (1999), pp. 11--20.
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D. Calvetti, B. Lewis and L. Reichel
On the selection of poles in the single input pole placement problem
Linear Algebra Appl., 302-303 (1999), pp. 331--345.
G.S. Ammar, D. Calvetti, W.B. Gragg and L. Reichel
Polynomial zerofinders based on Szego polynomials
J. Comput. Appl. Math., 127 (2001), pp. 1--16.
D. Calvetti, B. Lewis and L. Reichel
Partial eigenvalue assignment for large observer problems
Proceedings CD of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems, Perpignan, France, 2000, 5 pages.
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D. Calvetti, B. Lewis and L. Reichel
Partial eigenvalue assignment for large linear control systems
Structured Matrices in Operator Theory, Numerical Analysis, Control, Signal and Image Processing, ed. V. Olshevsky, Contemporary Mathematics, Amer. Math. Soc., Providence, RI, 2001, to appear.
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D. Calvetti, B. Lewis and L. Reichel
On the solution of large Sylvester-observer equations
Numer. Linear Algebra Appl., to appear.

Approximation theory

D. Calvetti, E. Gallopoulos and L. Reichel
Accuracy control for parallel evaluation of matrix rational functions
Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, eds. R.F. Sincovec, D.E. Keyes, M.R. Leuze, L.R. Petzold and D.A. Reed, SIAM, Philadelphia, 1993, pp. 652--655.

Numerical Methods for Ordinary and Partial Differential Equations

D. Calvetti, E. Gallopoulos and L. Reichel
Incomplete partial fractions for parallel evaluation of rational matrix functions
J. Comp. Appl. Math., 59 (1995), pp. 349--380.
D. Calvetti and L. Reichel
Exponential integration methods for large stiff systems of differential equations
Iterative Methods in Scientific Computing IV, eds. D.R. Kincaid and A.C. Elster, IMACS Series in Computational and Applied Mathematics, vol. 5, IMACS, New Brunswick, 1999, pp. 237--243.