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ACM Transactions on Mathematical Software (TOMS), Volume 39 Issue 4, July 2013

Scaling LAPACK panel operations using parallel cache assignment
Anthony M. Castaldo, R. Clint Whaley, Siju Samuel
Article No.: 22
DOI: 10.1145/2491491.2491492

In LAPACK many matrix operations are cast as block algorithms which iteratively process a panel using an unblocked algorithm and then update a remainder matrix using the high performance Level 3 BLAS. The Level 3 BLAS have excellent scaling, but...

Evaluating an element of the Clarke generalized Jacobian of a composite piecewise differentiable function
Kamil A. Khan, Paul I. Barton
Article No.: 23
DOI: 10.1145/2491491.2491493

Bundle methods for nonsmooth optimization and semismooth Newton methods for nonsmooth equation solving both require computation of elements of the (Clarke) generalized Jacobian, which provides slope information for locally Lipschitz continuous...

Reducing the influence of tiny normwise relative errors on performance profiles
Nicholas J. Dingle, Nicholas J. Higham
Article No.: 24
DOI: 10.1145/2491491.2491494

It is a widespread but little-noticed phenomenon that the normwise relative error ‖x - y‖/‖x‖ of vectors x and y of floating point numbers of the same precision, where y is an...

On Ziv's rounding test
Florent de Dinechin, Christoph Lauter, Jean-Michel Muller, Serge Torres
Article No.: 25
DOI: 10.1145/2491491.2491495

A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f(x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be...

Optimized code generation for finite element local assembly using symbolic manipulation
Francis P. Russell, Paul H. J. Kelly
Article No.: 26
DOI: 10.1145/2491491.2491496

Automated code generators for finite element local assembly have facilitated exploration of alternative implementation strategies within generated code. However, even for a theoretical performance indicator such as operation count, an optimal...

Algorithm 929: A suite on wavelet differentiation algorithms
Mani Mehra, Kavita Goyal
Article No.: 27
DOI: 10.1145/2491491.2491497

A collection of the Matlab routines that compute the values of the scaling and wavelet functions (&phis;(x) and ψ(x) respectively) and the derivative of an arbitrary function (periodic or non periodic) using wavelet bases is...

Algorithm 930: FACTORIZE: An object-oriented linear system solver for MATLAB
Timothy A. Davis
Article No.: 28
DOI: 10.1145/2491491.2491498

The MATLAB™ backslash (x=A\b) is an elegant and powerful interface to a suite of high-performance factorization methods for the direct solution of the linear system Ax = b and the least-squares problem minx...