Subject: NA Digest, V. 93, # 25 NA Digest Sunday, July 11, 1993 Volume 93 : Issue 25 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Alston Householder A Latex Question Information about GMRES Algorithm Programs from Book by Silebi and Schiesser COLDAE Available from NETLIB UMFPACK: General Unsymmetric Sparse Matrix Solver Spectral Multi-Domain Methods Workshop 12th Householder Symposium Contents: Constructive Approximation Contents: IMA Journal of Numerical Analysis Contents: Advances in Computational Mathematics Contents: Numerical Algorithms Contents: SIAM Numerical Analysis Submissions for NA Digest: Mail to na.digest@na-net.ornl.gov. Information about NA-NET: Mail to na.help@na-net.ornl.gov. ------------------------------------------------------- From: Gene Golub Date: Thu, 8 Jul 93 22:04:19 PDT Subject: Alston Householder Alston Householder died od a massive stroke on Sun, Jul 4. He was 89 years old. Those of us who attended the Householder meeting at Lake Arrowhead were fortunate to see him before he passed away. Householder made many contributions to linear algebra and numerical analysis. Many techniques that we use so easily were originated by him. But beyond his technical skill, he was a kind and gentle soul. He was modest and being in his presence was uplifting. He never denigrated others. Letters of condolence can be sent to his widow, Heidi Householder, 6235 Tapia drive, Malibu, CA 90265 or his son, Dr. John Householder, 743 North A Street, Oxnard, CA 93030. If you prefer, send an e-mail to me and I will send copies to Heidi and John. ( There is a surviving daughter but I do not know her address; she lives in Britain). We will organize a memorial fund at a later date. Gene ------------------------------ From: Mustafa Pinar Date: Mon, 5 Jul 93 10:14:28 CET Subject: A Latex Question I have the following question for Latex experts: I have a number of abstracts that I am trying to put together in a booklet. This can be done using the include or input commands. However, I would like to produce a table of contents with the correct page numbers at the beginning. But Latex requires -- to my knowledge -- that each separate file is treated as a section or a chapter to include it in the table of contents. I do not want to number each abstract. Is anybody familiar with a way to do this? I would appreciate any help. Mustafa Pinar Institute for Numerical Analysis TUD ------------------------------ From: Manuel Galan Moreno Date: Mon, 5 Jul 93 16:09:53 +0100 Subject: Information about GMRES Algorithm I would appreciate any information about papers or books on Y. Saad's GMRES(k) algorithm for solving linear systems. Also any information on vector/parallel implementations. Thanks. Manuel Galan manolo@titan.ulpgc.es ------------------------------ From: W. E. Schiesser Date: Mon, 5 Jul 1993 14:25:40 -0500 (CDT) Subject: Programs from Book by Silebi and Schiesser The programs in the book "Dynamic Modeling of Transport Process Systems" C. A. Silebi and W. E. Schiesser Academic Press, San Diego, 1992 including the programs for the problems at the ends of the chapters, are available on a 3.5 inch, DOS-formatted diskette. The programs generally implement numerical solutions to ODEs and PDEs as applied to problems in engineering and the physical sciences, particularly the dynamics of momentum, heat and mass transfer and reaction kinetics. Requests can be sent to: W. E. Schiesser (until August 22, 1993): SSC Laboratory, MS4003 Accelerator Division 2550 Beckleymeade Avenue Dallas, TX 75237 (214) 708-3525 (phone) (214) 708-4804 (fax) wes1@sscvx1.ssc.gov (Internet) (after August 25, 1993): Lehigh University Iacocca Hall, Room D307 111 Research Drive Bethlehem, PA 18015 USA (215) 758-4264 (office) (215) 758-5057 (fax) (215) 758-5297 (fax) wes1@lehigh.edu (Internet) ------------------------------ From: Uri Ascher Date: 5 Jul 93 13:01 -0700 Subject: COLDAE Available from NETLIB The code COLDAE is now available from netlib. (Say "send coldae from ode" in your e-mail message to netlib in order to get it.) This code, written by Ray Spiteri and myself, is an extension of the fortran code COLSYS/COLNEW. It attempts to solve multipoint boundary value systems of semi-explicit differential-algebraic equations of index at most 2 (this includes fully implicit index-1 daes and boundary value odes as special cases). It uses projected collocation at Gaussian points and does automatic mesh selection and error control of the differential solution components. A paper describing the various techniques involved will appear some day in SIAM's SISC. Enjoy! Uri Ascher ------------------------------ From: Tim Davis Date: Tue, 6 Jul 93 11:15:17 -0400 Subject: UMFPACK: General Unsymmetric Sparse Matrix Solver UMFPACK: Unsymmetric-pattern MultiFrontal Package The Unsymmetric-pattern MultiFrontal Package (UMFPACK) solves Ax=b using LU factorization, where A is a general unsymmetric sparse matrix. The method relies on dense matrix kernels (the BLAS) to factorize rectangular frontal matrices, which are dense submatrices of the sparse matrix being factorized. UMFPACK is available via netlib ("send umfpack.shar from misc") or anonymous ftp (ftp.cis.ufl.edu:pub/umfpack). Both single- and double-precision ANSI Fortran-77 versions are included. UMFPACK is freely available for research purposes. For commercial use, please contact Tim Davis. In one of our extensions to the method, we are investigating a distributed memory, factor-only version that would be used to factor a sequence of matrices that have an identical sparsity pattern. In order to evaluate the performance and effectiveness of these extensions, we are in search of realistic test problems that produce sequences of matrices with identical and unsymmetric sparsity patterns. Matrices of order greater than 1000 are of most interest. If you have or know of such test problems, please contact Tim Davis (davis@cis.ufl.edu) or Steve Hadfield (smh@cis.ufl.edu). Tim Davis, Computer and Info. Sci. Dept., Univ. of Florida, Gainesville, FL. Joint work with Iain Duff, Rutherford Appleton Laboratory, England, and CERFACS, Toulouse, France. ------------------------------ From: Kelly Black Date: Mon, 5 Jul 93 09:26:47 -0400 Subject: Spectral Multi-Domain Methods Workshop Preliminary Summary for Spectral Multi-Domain Methods Workshop May 16-18, 1994 Center for Research in Scientific Computing North Carolina State University Raleigh, North Carolina, USA Topic: Interface conditions for spectral multi-domain methods. There is an intricate balance between what happens at the interfaces and the trade-offs between the discretization and the actual implementation. This is further compounded when considering different computational architectures. The topics are not limited to these concerns and may also include topics that reflect the interests of the speakers. Our primary interest is to provide a forum for attendees to freely exchange ideas with a view to collaboration. Format: We anticipate each speaker providing an introductory lecture and a lecture on their area of expertise. The introductory lectures can be coordinated so that topics central to spectral multi-domain techniques are covered. Presentations are limited to the invited speakers; however, there will be a poster session. Also, the number of attendees will be limited in the interest of providing a more intimate setting. Organizing committee: Kelly Black North Carolina State University Wei Cai University of North Carolina, Charlotte Jeffrey S. Scroggs North Carolina State University Scientific committee: H.T. Banks North Carolina State University Paul Fischer Brown University List of speakers (tentative): Paul Fischer Brown University Daniele Funaro Universita di Pavia David Gottlieb Brown University George Karniadakis Princeton University Steven Orszag Princeton University For more information, please contact Kelly Black Center for Research in Scientific Computing Box 8205, North Carolina State University Raleigh, North Carolina, 27695-8205, USA (919)515-5289 smd94@wave.math.ncsu.edu ------------------------------ From: Stephen Vavasis Date: Wed, 7 Jul 93 14:12:41 -0400 Subject: 12th Householder Symposium The 12th Householder Symposium on Numerical Algebra was held in Lake Arrowhead, California during the week of June 14. The Householder Symposium, which was formerly known as the Gatlinburg Conference, was renamed in 1990 in honor of Alston S. Householder and is held once every three years. Householder, who attended the 1993 meeting, organized four Gatlinburg Conferences at the beginning the series and is known for his pioneering work in numerical linear algebra. Gene Golub recently reported the sad news that Householder passed away in July. The meeting, which was organized by Tony Chan of UCLA and Gene Golub of Stanford, was the largest ever in the series, with approximately 160 participants. It has been traditional to hold the meeting in an isolated venue--Lake Arrowhead is located in the mountains 60 miles east of Los Angeles--in order to promote informal interaction. The meeting was funded in part by the National Science Foundation and The Mathworks, Inc. Babette Dalton of UCLA helped organize much of the logistics of the meeting. Highlighting the 1993 meeting was the presentation of two Householder awards for the best PhD dissertation in numerical linear algebra during the past three years. The two winners were Barry Smith and Hong-Guo Xu. Smith, who received his PhD in mathematics from the Courant Institute of New York University in 1990, has worked in the area of domain decomposition and finite element methods. Domain decomposition refers to a class of numerical methods for solving boundary value problems by solving independent problems on subdomains and then numerically iterating to obtain a global solution. Smith's dissertation, which was advised by Olof Widlund, contains new, optimal results on convergence rates for domain decomposition applied to problems where the subdomains do not have significant overlap and where the coefficients are varying. Smith was the Wilkinson Fellow at Argonne National Laboratory following the awarding of his PhD, and is currently in the mathematics department of UCLA. Xu received his PhD in mathematics from Fudan University, Shanghai, in 1991. His dissertation, which was advised by Jiang Er-xiong, focuses on numerical solution of the Riccati equations. In his thesis, he derived structured algorithms for the solution of both continuous time and discrete time algebraic Riccati equations. These algorithms are based on a simple but elegant proof of the existence of particular square roots of matrices with Hamiltonian or symplectic structure. Xu derived an error analysis and showed how to use iterative refinement for ill-conditioned Riccati equations. He also conducted thorough testing of the new algorithms to verify theoretical error bounds. Xu is currently in the mathematics department of Fudan University. Beresford Parlett, speaking for the Householder award committee, said that the criteria were mathematical innovation, computational experiments, and applicability of the results. The committee also decided to select one nominee, Ali Sayed, for a special mention. Sayed received his PhD in August of 1992 in electrical engineering under the direction of Thomas Kailath. His dissertation describes how a variant of Gaussian elimination can be applied to a variety of problems in linear algebra and control theory, including Toeplitz systems and Pade tables, to yield efficient algorithms. The key concept in the dissertation is a generalization of "low displacement rank." Sayed's work unifies many previous and seemingly complicated algorithms in the literature. Sayed is headed for the electrical engineering department of UCSB. The bulk of the meeting was 30 plenary lectures spread over five days. The lectures covered various topics of current interest, including parallel linear algebra, sparse systems, boundary value problems, updating and downdating factorizations, perturbation bounds, and structured systems. Many of the talks described applications of linear algebra, including applications to partial differential equations and signal and image processing. In addition to the plenary lectures, there were concurrent sessions in the evenings on topics such as parallel computation, multigrid and domain decomposition methods, eigenvalue algorithms, and others. The meeting opened with plenary talks by Paul Van Dooren, Hong-yuan Zha and Sabine Van Huffel on matrix factorizations arising in signal processing and statistics. Van Dooren spoke on numerically stable simultaneous factorization of a product of matrices arising in control. Algorithms for canonical correlations arising in statistics was the subject of Zha's presentation. Van Huffel compared structured total least squares to constrained total least squares, and applied them to biomedical problems. A sequence of talks by James Demmel, Roy Mathias, and Nick Higham focused on the relationship between parallelism and numerical stability in linear algebra. Demmel described an eigenvalue toolkit using new algorithms based on the matrix sign function. The method, though ideal for parallelism, has weaker stability properties compared to traditional sequential methods. Mathias showed that computing signatures by parallel prefix methods was less stable than traditional accumulation. Parallel triangular solvers were the subject of Nick Higham's talk; he showed that several proposed algorithms are not as stable as sequential back-substitution. Two speakers addressed sparse matrix methods. John Gilbert described implementation and experimentation with geometric mesh partitioning, important for parallel iterative methods and sparse Gaussian elimination in finite element problems. Stan Eisenstat described new approaches to sparse unsymmetric factorization that attempt to incorporate successful ideas from symmetric algorithms. Several talks focused on iterative algorithms for solving nonsymmetric and indefinite linear systems. Gerald Sleijpen showed how to prevent stagnation in the BiCGSTAB iterative algorithm in an extension denoted BiCGSTAB(l). Anne Greenbaum described a new analysis of the GMRES algorithm that can better distinguish matrices for which the method will converge quickly. Michael Saunders compared two iterative methods, LSQR and Craig's method, showing equivalence in some cases. Boundary value problems were the subject of three talks. Steve Vavasis proposed new elimination methods for solving boundary value problems that are guaranteed to be numerically stable in the presence of wild variation in the coefficient field. Andy Wathen proposed new preconditioned iterative methods for Stokes' flow with optimal bounds on the condition number. Coincidentally, both of these speakers analyzed properties of the symmetric indefinite linear system [H, A' ; A, 0] to obtain their results. Hans Munthe-Kaas showed how to unify various fast Poisson solvers in terms of abelian groups. A number of talks focused on updating, downdating, and rank-detection algorithms. These algorithms are very important in signal processing, where it is necessary to maintain information such as numerical rank for a time-varying signal. In a time-varying signal, "old" information must somehow be eliminated from the factorization and rank approximations as time passes. C.-T. Pan spoke on recent progress in rank-revealing QR factorization, which is used as an efficient substitute for the full singular-value decomposition. Haesun Park spoke on a hybrid, more stable method for downdating the URV decomposition, also used for monitoring numerical rank. Ming Gu proposed new algorithms for downdating the singular-value decomposition itself. Frank Luk derived a new factorization of matrix pairs amenable to updating. Chris Paige delivered the banquet plenary address on the history of the C-S decomposition and angles between subspaces. His talk showed a history going back to Jordan, and focused on recent contributions by C. Davis, W. Kahan and G. W. Stewart. Perturbation theory was the subject of several talks. Michael Overton discussed a new way to analyze stability in Hamiltonian systems; the stability issue can be expressed as an eigenvalue perturbation problem. Ji-guang Sun gave new backwards-perturbation estimates for a wide variety of least-squares and eigenvalue problems that are the best possible estimates in many cases. Ilse Ipsen showed a new method for analyzing a variety of eigenvalue perturbation problems; her method is based on writing additive perturbations as matrix multiplications. Nick Trefethen presented experimental comparisons between how perturbations of the coefficients affect the zeros of a polynomial, and how perturbations of a companion matrix affect its eigenvalues. The results seem to be very similar, but only if "balancing" is used on the companion matrix. Three speakers addressed ill-posed problems. Jay Kuo discussed the use of wavelets in image compression and processing. Bob Plemmons described new preconditioners for iterative methods used in image recovery. Per Christian Hansen discussed a new analysis for determining when and how conjugate gradient can reveal a regularized solution for ill-posed problems. Three talks focused on analysis of structured problems. Zdenek Strakos spoke on the relation between numerical errors in Gaussian quadrature computation and the Lanczos iteration. Roland Freund spoke on stabilizing "fast" algorithms (that is, O(n^2) flops) for Toeplitz systems using look-ahead procedures. Martin Gutknecht described new "superfast" algorithms (that is, O(n (log n)^2) flops) for the same problems. Leslie Foster in his talk gave examples arising in differential and integral equations for which Gaussian elimination with partial pivoting (GEPP) is numerically unstable. It has been known since Wilkinson's work that, theoretically, GEPP can be unstable because of the "growth factor," but many researchers have believed that this instability does not occur in practical problems. Because of examples like Foster's and other recent works, implementors of GEPP including the LAPACK designers are planning to build additional safeguards into software to detect unstable behavior. In addition to these plenary talks, there were a total of 18 informal sessions spread over three evenings. One very popular session was organized by Cleve Moler to demonstrate upcoming developments in Matlab, which is an interactive software package for numerical computation by The Mathworks, Inc. Moler demonstrated some of the features of the latest version of Matlab and gave a preview of a toolbox under development that integrates Maple, a symbolic mathematics package from University of Waterloo, with Matlab. Underscoring the informal nature of the meeting, one session (on geometry, eigenvalues, and optimization, organized by Alan Edelman) was held at the conference center's outdoor picnic area. For the first time at a Householder meeting, laptop computers played an important scientific role as many participants demonstrated software to one another and conducted experiments during the breaks. One use of the laptops, which were provided by UCLA and Cleve Moler, was to analyze an impromptu graph made at the meeting showing coauthorship relationships among participants. The graph was started by Nick Trefethen, but most of the participants joined in. Gene Golub turned out to have by far the greatest number of coauthors. In addition to the technical presentations, there were many recreational activities available at the scenic conference site. Boat tours for the participants showed off the beauty of Lake Arrowhead and the surrounding palatial summer homes owned by movie stars. Petter Bjorstad led 16 people on a hike up Mount San Gorgonio, six of whom went to the summit at 11,499 feet. Two milestones were celebrated at the meeting. Gene Golub was feted for his recent election to the National Academy of Sciences, and Alan Edelman turned 30 at the meeting. Congratulations to Gene and Alan! Charlie Van Loan collected funds from participants for a gift certificate for Babette Dalton to thank her for her hard work on organization. The next Householder meeting is scheduled for 1996 in Switzerland. As Martin Gutknecht said, the organizers of the Lake Arrowhead meeting, including Tony Chan, Gene Golub and Babette Dalton, have set a high standard for future organizers! ------------------------------ From: E. B. Saff Date: Wed, 7 Jul 93 16:13:12 EDT Subject: Contents: Constructive Approximation CONSTRUCTIVE APPROXIMATION contents Volume 9 Number 4 1993 Robert Schaback Planar Curve Interpolation by Piecewise Conics of Arbitrary Type Yongsheng Sun and Yongpins Liu Optimal Recovery of the Sobolev-Wiener Class of Smooth Functions by Double Sampling R.K. Beatson and W.A. Light Quasi-interpolation by Thin-Plate Splines on a Square S.P. Zhou On Muntz Rational Approximation P. Binev, P. Petrushev, E.B. Saff, and O. Trifonov Distribution of Interpolation Points of Best L_2-Approximants Glenn M. Lilly and Stephen C. Milne The C_l Bailey Transform and Bailey Lemma Thomas Bagby, Aurel Cornea, and P.M. Gauthier Harmonic Approximation on Arcs J. Borwein, P. Borwein, and F. Garvan Hypergeometric Analogues of the Arithmetic-Geometric Mean Iteration Serge Dubuc and Fahima Nekka General Interpolation Schemes for the Generation of Irregular Surfaces D.J. Newman and Yuan Xu Tchebycheff Polynomials on a Triangular Region ------------------------------ From: Iain Duff Date: Mon, 5 Jul 93 10:23:04 GMT Subject: Contents: IMA Journal of Numerical Analysis IMA Journal of Numerical Analysis. Volume 13 Number 3. July 1993. Raydan M On the Barzilai and Borwein choice of steplength for the gradient method. Coope I D Curve interpolation with nonlinear spiral splines. Tsao N K and Sun T C On the numerical computation of the derivatives of a B-spline series. Hu Y An algorithm for data reduction using splines with free knots. Williams J and Kalogiratou Z Best Chebyshev approximation from families of ordinary differential equations. Hosea M E and Shampine L F Global extrapolation integrators for solving Sturm-Liouville problems by shooting. Huang W and Sloan D M A new pseudospectral method with upwind features. Manoranjan V S and Drake R A spectrum enveloping technique for convection-diffusion computations. Elliott D An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals. Rodriguez G and Seatzu S On the numerical inversion of the Laplace transform in reproducing kernel Hilbert spaces. Koehler P Error estimates for generalized compound quadrature formulas. ------------------------------ From: Laurenz Baltzer Date: Tue, 6 Jul 1993 14:42:08 +0200 Subject: Contents: Advances in Computational Mathematics Contents ADVANCES IN COMPUTATIONAL MATHEMATICS Editors-in-Chief: John C. Mason Applied & Computational Mathematics Group Royal Military College of Science Shrivenham, Swindon, SN6 8LA UNITED KINGDOM e-mail: mason@rmcs.cran.ac.uk Charles A. Micchelli Mathematical Sciences Department IBM Research Center P.O. Box 218 Yorktown Heights, NY 10598 U.S.A. e-mail: cam@yktvmz.bitnet Volume 1, no. 1 W. Dahmen & C.A. Micchelli, Continuous refinement equations and subdivision P.J. van der Houwen, Preconditioning in implicit initial value problem methods on parallel computers H.N. Mhaskar, Approximation properties of a multilayered feedforward artificial neural network A.R. Champneys & A. Spence, Hunting for homoclinic orbits in reversible systems: a shooting technique T.N.T. Goodman, S.L. Lee & W.S. Tang, Wavelet bases for a set of commuting unitary operators R.E. Bank & C.C. Douglas, Sparse matrix multiplication package (SMMP) Volume 1, no. 2 P.J. Barry, R.N. Goldman & C.A. Micchelli, Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices J.M. Carnicer & J. M. Pena, Shape preserving representations and optimality of the Bernstein basis R.A. DeVore, G. Kyriazis, D. Leviaton & V.M. Tikhomirov, Wavelet-compression and nonlinear n-widths D.E. Gonsor, Nonnegative masks and stationary subdivision W.B. Liu & J.W. Barrett, Error bounds for the finite element approximation of a degenerate quasilinear parabolic variational inequality L. Reichel, Construction of polynomials that are orthogonal with respect to a discrete bilinear form Orders and requests for sample copies to be sent to J.C. Baltzer AG, Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland, fax: +41-61-692-42-62, e-mail: publish@baltzer.nl Laurenz Baltzer J.C.Baltzer AG, Science Publishers Asterweg 1A 1031 HL Amsterdam The Netherlands Tel: +31 20 6370061 Fax: +31 20 6323651 E-mail: publish@baltzer.nl ------------------------------ From: Laurenz Baltzer Date: Tue, 6 Jul 1993 14:47:26 +0200 Subject: Contents: Numerical Algorithms Contents NUMERICAL ALGORITHMS Editor-in-Chief: Claude Brezinski Laboratoire d'Analyse Numerique et d'Optimization UFR IEEA - M3 Universite des Sciences et Techniques de Lille 59655 Villeneuve d' Ascq Cedex FRANCE fax: +33-20-43-49-95 e-mail: brezinsk@frcitl81.bitnet VOLUME 4, NO. 3: Y. Xu, W.A. Light and E.W. Cheney, Constructive methods of approximation by ridge functions and radial functions P. Levrie and A. Bultheel, A note on Thiele n-fractions M.A. Diniz-Ehrhardt and J.M. Martinez, A parallel projection method for overdetermined nonlinear systems of equations Nguyen huu Cong, A-stable diagonally implicit Runge-Kutta-Nystrom methods for parallel computers M. Calvo, J.I. Montijano and L. Randez, On the change of step size in multistep codes VOLUME 4, NO. 4: S. Durand, Convergence of cascade algorithms introduced by I. Daubechies K. Strom, Products of B-patches C. Clavero and F. Lisbona, Uniformly convergent finite difference methods for singularly perturbed problems with turning points K. Jbilou, A general projection algorithm for solving systems of linear equations P. Joly and G. Meurant, Complex conjugate gradient methods Orders and requests for sample copies to be sent to J.C. Baltzer AG, Science Publishers, Wettsteinplatz 10, CH-4058 Basel, Switzerland, fax: +41-61-692-42-62, e-mail: publish@baltzer.nl Laurenz Baltzer J.C.Baltzer AG, Science Publishers Asterweg 1A 1031 HL Amsterdam The Netherlands Tel: +31 20 6370061 Fax: +31 20 6323651 E-mail: publish@baltzer.nl ------------------------------ From: SIAM Date: Tue, 06 Jul 93 11:40:15 EST Subject: Contents: SIAM Numerical Analysis Table of Contents SIAM J. Numer. Anal., 30-5 October 1993 The Relative Efficiency of Alternative Defect Control Schemes for High Order Continuous Runge--Kutta Formulas W. H. Enright Second-Order Accurate Difference Methods for a One-Sex Model of Population Dynamics Yong Hoon Kwon and Chung-Ki Cho Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem Relja Vulanovic and Paul A. Farrell New Error Bounds for the Quadrature Method for the Solution of Cauchy Singular Integral Equations Dietmar Berthold and Peter Junghanns Sizing and Least Change Secant Methods J. E. Dennis, Jr. and H. Wolkowicz Need Title Krishna and Wang Domain Decomposition Type Iterative Techniques for Parabolic Problems on Locally Refined Grids R. E. Ewing, R. D. Lazarov, J. E. Pasciak, and P. S. Vassilevski On the Identification Property of a Projected Gradient Method P. L. De Angelis and G. Toraldo Convergence Rates for Maximum Entropy Regularization Heinz W. Engl and Gerhard Landl A Stability Result for Sectorial Operators in Banach Spaces C. Palencia Quadtrature Methods for Strongly Elliptic Equations of Negative Order on Smooth Closed Curves J. Saranen and L. Schroderus Ordering Effects of Relaxation Methods Applied to the Discrete One- Dimensional Convection-Diffusion Equation Howard C. Elman and Michael P. Chernesky FFT-Based Preconditioners for Toeplitz-Block Least Squares Problems Raymond H. Chan, James G. Nagy, and Robert J. Plemmons Godunov-Mixed Methods for Advection-Diffusion Equations in Multidimensions Clint Dawson Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems O. Scherzer, H. W. Engl, and K. Kunisch Differential Interpolants for High-Order Runge--Kutta Methods J. H. Verner On Entropy Consistency of Large Time-Step Schemes I. The Godunov and Glimm Schemes Gerald Warnecke and Jinghua Wang On Entropy Consistency of Large Time-Step Schemes II. Approximate Riemann Solvers Gerald Warnecke and Jinghua Wang Convergence Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints Edda Eich A Dissipative Pseudo-Spectral Method for the Two-Dimensional Navier--Stokes Equations K. Ito and S. Kang ------------------------------ End of NA Digest ************************** -------