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Unified form language: A domain-specific language for weak formulations of partial differential equations
Martin S. Alnæs, Anders Logg, Kristian B. Ølgaard, Marie E. Rognes, Garth N. Wells
Article No.: 9
We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and...
Computing the sparsity pattern of Hessians using automatic differentiation
Robert Mansel Gower, Margarida Pinheiro Mello
Article No.: 10
We compare two methods that calculate the sparsity pattern of Hessian matrices using the computational framework of automatic differentiation. The first method is a forward-mode algorithm by Andrea Walther in 2008 which has been implemented as the...
The algorithm that computes the midpoint of an interval with floating-point bounds requires some careful devising to handle all possible inputs correctly. We review several implementations from prominent C/C++ interval arithmetic...
Optimally packed chains of bulges in multishift QR algorithms
Lars Karlsson, Daniel Kressner, Bruno Lang
Article No.: 12
The QR algorithm is the method of choice for computing all eigenvalues of a dense nonsymmetric matrix A. After an initial reduction to Hessenberg form, a QR iteration can be viewed as chasing a small bulge from the top left to the bottom...
A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc
Eloy Romero, Jose E. Roman
Article No.: 13
In the context of large-scale eigenvalue problems, methods of Davidson type such as Jacobi-Davidson can be competitive with respect to other types of algorithms, especially in some particularly difficult situations such as computing interior...
Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions
J. Tilak Ratnanather, Jung H. Kim, Sirong Zhang, Anthony M. J. Davis, Stephen K. Lucas
Article No.: 14
A MATLAB toolbox, IIPBF, for calculating infinite integrals involving a product of two Bessel functions Ja(ρx)Jb(τ x), Ja(ρ...
A code is presented which offers a simple clean way to get output that is very easy to read. Special support is given for the output of error messages which are a part of an application package or subprogram library. The code uses many of the...
Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems
Sou-Cheng T. Choi, Michael A. Saunders
Article No.: 16
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the...
Data sequences generated by on-line sensors can become arbitrarily large and must, therefore, be pared down to fit into available memory. For situations where only the most recent data is of interest, this problem can be solved with optimal...