Subject: NA Digest, V. 93, # 27 Subject: NA Digest, V. 93, # 27 NA Digest Sunday, July 25, 1993 Volume 93 : Issue 27 Today's Editor: Cleve Moler The MathWorks, Inc. moler@mathworks.com Today's Topics: Moving Boundary Problems Elliptic PDE Solver Sought Numerical Mathematics, A Laboratory Approach Eigensystem Solver for Pentadiagonal Systems Workshop at Bath Post Doc Position at Battelle Pacific Northwest Laboratory Contents: Linear Algebra and its Applications 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: Pasqua D'Ambra Date: Thu, 22 Jul 93 13:26:13 EDT Subject: Moving Boundary Problems I am a Ph.D. Student and I am working on my thesis. The subject is "Moving boundary problems (Stefan Problems)". I would like to have contacts with other researchers in the field and I would like to receive recent references about resolution of these problems on parallel machines. PASQUA D'AMBRA PHONE: +39 81 675624 Universita' di Napoli FAX : +39 81 7662106 dip. matematica e applicazioni E-MAIL: PASQUA@VM.CISED.UNINA.IT 80126 Napoli Italia ------------------------------ From: Vladimir Oliker Date: Mon, 19 Jul 93 09:32:37 -0400 Subject: Elliptic PDE Solver Sought I am looking for a high accuracy linear elliptic PDE-solver that can deal with general boundary conditions in 2-d domains with curved boundaries; for example, on an ellipse. Any help will be greatly appreciated. Vladimir Oliker oliker@mathcs.emory.edu ------------------------------ From: Eugene Isaacson Date: Tue, 20 Jul 1993 16:18:42 -0500 (EST) Subject: Numerical Mathematics, A Laboratory Approach Just Published. "Numerical Mathematics - A Laboratory Approach", by Shlomo Breuer & Gideon Zwas Cambridge University Press, 267 p. Most noteworthy for its unique use of the microcomputer laboratory to treat algorithmic aspects of mathematics - without calculus or linear algebra. Here is a mathematically rigorous development in eight chapters: 1. Mathematics in a numerical laboratory; 2. Iterations for root extractions; 3. Area approximations; 4. Linear systems - an algorithmic approach; 5. Algorithmic computations of pi and e; 6. Convergence acceleration; 7. Interpolative approximation; 8. Computer library functions. Suitable for first year college students; training mathematics teachers; and gifted high school students. ------------------------------ From: Imran Bhutta Date: Wed, 21 Jul 93 11:20:56 EDT Subject: Eigensystem Solver for Pentadiagonal Systems Dear Editor(s), I am developing a Semiconductor Device Simulator using Quantum Mechanical approach. It is a 2-D simulator and at one point involves the solution of the Schrodinger's equation. That is to say I have to find the eigenvalues and corresponding eigenvectors for that system of equations. For a 2-D system with 100 points in 'x' and 'y' directions, my eigen system matrix is a n**2 by n**2 i.e., 10,000 by 10,000. This matrix is a pentadiagonal matrix, with a diagonal vector and two subdiagonals and two superdiagonals. The subdiagonals lie at 'i-1' and 'i-5' and the superdiagonals lie at 'i+1' and 'i+5'. It is a highly sparse matrix, which is real and symmetric. I am looking for a routine that would help me solve this pentadiagonal eigen system. I have routines for tridiagonal systems, and my first approach was to reduce my pentadiagonal matrix to a tridiagonal form by Householder's scheme. However Householder's scheme generates an orthogonal matrix alongwith the tridiagonal matrix, and I do not gain any advantage in space saving, since the orthogonal matrix is not pentadiagonal. If someone can suggest a solution technique I would appreciate it very much. My e-mail address is BHUTTA@VTVM1.CC.VT.EDU. I appreciate your help very much. Thank you. Imran A. Bhutta EE Department Virginia Tech Blacksburg, VA 24061-0111 ------------------------------ From: I. G. Graham Date: Mon, 19 Jul 93 9:57:34 BST Subject: Workshop at Bath Dear Colleagues, This is to inform you that there will be an informal workshop on iterative methods for PDE at the University of Bath, U.K. on September 6th 1993. The two principal speakers are Professor Wolfgang Hackbusch (University of Kiel, Germany) and Professor Dan Sorensen (Rice University, Texas). There will also be a number of contributed talks from U.K. researchers. Best wishes, Ivan Graham (igg@maths.bath.ac.uk) Iterative methods for large computational problems arising from PDEs A Workshop at the University of Bath Monday 6th September 1993 -- Building 6E, Room 2.2 Wolfgang Hackbusch (Christian Albrechts Universit\"{a}t, Kiel, Germany): On the frequency decomposition multi-grid method. Kevin Parrott and Tony Ware (Oxford University Computing Laboratory): Parallel multi-grid for a 3-D tensor diffusion problem with block-discontinuous coefficients Mike Wilson (School of Mechanical Engineering, University of Bath): Parallel multi-grid computation of rotating disc flows Paul Crumpton (Oxford University Computing Laboratory): Multi-grid for non-nested grids on a parallel computer Dan Sorensen (Rice University): Variations on Arnoldi's method for large scale eigenvalue problems Mark Hagger and Alastair Spence (School of Mathematical Sciences, Bath): Polynomial preconditioning for conjugate gradient methods Rob Coomer and Ivan Graham (School of Mathematical Sciences, Bath): Mesh-independent fixed point iteration and domain decomposition for semiconductor device equations in 2D All interested persons are welcome to attend. There will be no registration fee. However, in order that we can inform the catering department about the numbers for lunch it would be helpful if those who intend to come could inform us before August 27th by email to Ivan Graham at igg@maths.bath.ac.uk or by telephone to Sarah Love at (0225) 826198 or School of Mathematical Sciences, University of Bath, Bath BA2 7AY, U.K. ------------------------------ From: George Fann Date: Wed, 21 Jul 93 10:03:56 PDT Subject: Post Doc Position at Battelle Pacific Northwest Laboratory Post-doc Opening starting Oct. 1993 Battelle Pacific Northwest Laboratory The Analytic Sciences Department of the Pacific Northwest Laboratory is inviting applications for a postdoctoral research position. The appointment is initially for a one-year term. The successful candidate will participate in a project for computational fluid dynamics and numerical linear algebra algorithms for MIMD parallel computers ( e.g. Touchstone DELTA, or clusters of HP 9000/735 and IBM RS6000/560 workstations). We are looking for an individual to implement and investigate recent algorithm advances in solving elliptic and parabolic equations using the finite volume formulation. This project is interdisciplinary in nature and interfaces with efforts in numerical analysis, parallel computing, large-scale simulation of physical processes, and programming tools. Project members have access to state-of-the art computing facilities, including a 520-processor Intel Touchstone DELTA. Nominal requirements include a Ph.D. in computer science, applied mathematics, or an applied science or engineering discipline. A good algorithms background and hands-on experience in some aspect of scientific computing is necessary. Applications must be addressed to George Fann, ms: K7-15 Pacific Northwest Laboratory, Battelle Blvd, Richland, WA 99352, or via e-mail to gi_fann@pnl.gov. The application must include a resume and the names and addresses of three references. For further information, contact George Fann, gi_fann@pnl.gov. Fax:(509) 375-3641. Battelle is an affirmative action/equal opportunity employer. Legal right to work in U.S. is required -- U.S. Citizenship preferred. Pacific Northwest Laboratory is a U.S. Department of Energy laboratory. ------------------------------ From: Richard Brualdi Date: Wed, 21 Jul 1993 08:36:20 -0500 (CDT) Subject: Contents: Linear Algebra and its Applications LINEAR ALGEBRA AND ITS APPLICATIONS Contents Volumes 188/189 Preface 1 Dario Bini (Pisa, Italy) and Victor Pan (Bronx, New York) Improved Parallel Computations With Toeplitz-like and Hankel-like Matrices 3 Adam W. Bojanczyk (Ithaca, New York), James G. Nagy (Dallas, Texas), and Robert J. Plemmons (Winston-Salem, North Carolina) Block RLS Using Row Householder Reflections 31 Stephen Boyd (Stanford, California) and Laurent El Ghaoui (Paris, France) Method of Centers for Minimizing Generalized Eigenvalues 63 Ralph Byers (Lawrence, Kansas) and N. K. Nichols (Reading, United Kingdom) On the Stability Radius of a Generalized State-Space System 113 Biswa Nath Datta and Fernando Rincon (De Kalb, Illinois) Feedback Stabilization of a Second-Order System: A Nonmodal Approach 135 Bart De Moor (Leuven, Belgium) Structured Total Least Squares and L2 Approximation Problems 163 Ludwig Elsner and Chunyang He (Bielefeld, Deutschland) Perturbation and Interlace Theorems for the Unitary Eigenvalue Problem 207 Michael K. H. Fan (Atlanta, Georgia) A Quadratically Convergent Local Algorithm on Minimizing the Largest Eigenvalue of a Symmetric Matrix 231 Roland W. Freund (Murray Hill, New Jersey) and Hongyuan Zha (University Park, Pennsylvania) Formally Biorthogonal Polynomials and a Look-ahead Levinson Algorithm for General Toeplitz Systems 255 Mei Gao and Michael Neumann (Storrs, Connecticut) A Global Minimum Search Algorithm for Estimating the Distance to Uncontrollability 305 Martin H. Gutknecht (Zurich, Switzerland) Stable Row Recurrences for the Pade Table and Generically Superfast Lookahead Solvers for Non-Hermitian Toeplitz Systems 351 A. Scottedward Hodel (Auburn, Alabama) Computation of System Zeros With Balancing 423 W. W. Lin (Hsin-Chu, Taiwan) and S. S. You (Chung-Li, Taiwan) A Symplectic Acceleration Method for the Solution of the Algebraic Riccati Equation on a Parallel Computer 437 Lin-Zhang Lu (Fujian, China) and Wen-Wei Lin (Hsinchu, Taiwan) An Iterative Algorithm of the Solution of the Discrete-Time Algebraic Riccati Equation 465 Alexander N. Malyshev (Novosibirsk, Russia) Parallel Algorithm for Solving Some Spectral Problems of Linear Algebra 489 Pradeep Misra (Dayton, Ohio) and Thulasinath Manickam (Kingston, Rhode Island) Balanced Realization of Separable-Denominator Multidimensional Systems 521 Marc Moonen (Heverlee, Belgium), Paul Van Dooren (Urbana, Illinois), and Filiep Vanpoucke (Heverlee, Belgium) On the QR Algorithm and Updating the SVD and the URV Decomposition in Parallel 549 W. H. L. Neven (Emmeloord, the Netherlands) and C. Praagman (Groningen, the Netherlands) Column Reduction of Polynomial Matrices 569 R. V. Patel (Montreal, Quebec, Canada) On Computing the Eigenvalues of a Symplectic Pencil 591 Vassilis Syrmos (Honolulu, Hawaii) and Petr Zagalak (Prague, Czechoslovakia) Computing Normal External Descriptions and Feedback Design 613 David H. Wood (Newark, Delaware) Product Rules for the Displacement of Near-Toeplitz Matrices 641 Dragan Zigic, Layne T. Watson, and Christopher Beattie (Blacksburg, Virginia) Contragredient Transformations Applied to the Optimal Projection Equations 665 Author Index 677 LINEAR ALGEBRA AND ITS APPLICATIONS Contents Volume 190 Jack B. Brown (Auburn, Alabama), Phillip J. Chase (Ft. Meade, Maryland), and Arthur O. Pittenger (Baltimore, Maryland) Order Independence and Factor Convergence in Iterative Scaling 1 James S. Otto (Denver, Colorado) Multigrid Convergence for Convection-Diffusion Problems on Composite Grids 39 Hassane Sadok (Villeneuve d'Ascq-Cedex, France) Quasilinear Vector Extrapolation Methods 71 Han H. Cho (Seoul, Korea) Prime Boolean Matrices and Factorizations 87 J. B. Wilker (Scarborough, Ontario, Canada) The Quaternion Formalism for Mobius Groups in Four or Fewer Dimensions 99 Martin Hanke (Karlsruhe, Germany) and Michael Neumann (Storrs, Connecticut) The Geometry of the Set of Scaled Projections 137 Joel E. Cohen (New York, New York) and Uriel G. Rothblum (Haifa, Israel) Nonnegative Ranks, Decompositions, and Factorizations of Nonnegative Matices 149 Carolyn A. Eschenbach (Atlanta, Georgia) and Charles R. Johnson (Williamsburg, Virginia) Sign Patterns That Require Repeated Eigenvalues 169 Raymond H. Chan and Kwok-Po Ng (Hong Kong, People's Republic of China) Toeplitz Preconditioners for Hermitian Toeplitz Systems 181 Roger A. Horn (Salt Lake City, Utah) and Dennis I. Merino (Hammond, Louisiana) A Real-Coninvolutory Analog of the Polar Decomposition 209 M. H. Lim (Kuala Lumpur, Malaysia) A Note on Similarity Preserving Linear Maps on Matrices 229 Miroslav Fiedler and Zdenek Vavrin (Praha, Czech Republic) Polynomials Compatible With a Symmetric Loewner Matrix 235 William A. Adkins (Baton Rouge, Louisiana), Jean-Claude Evard (Laramie, Wyoming), and Robert M. Guralnick (Los Angeles, California) Matrices Over Differential Fields Which Commute With Their Derivative 253 Author Index 263 Contents 190, September ------------------------------ End of NA Digest ************************** -------