Origin of Black-Box Operators

The question "where do black-box operators come from?" is really two different questions:

  1. Where do nature create problems with exploitable structure?
  2. Where do the black-box operators used in BBTools come from?

We answer the first question with a quotation from [20]:

Large matrices ... usually arise indirectly in the discretization of differential or integral equations. One might say, that if m is large, it is probably an approximation to . It follows that most large matrices of computational interest are simpler than their vast number of individual entries might suggest.

The operators used in BBTools generally have the following sources:

  1. Matlab-matrices converted to black-box operators
  2. Operators constructed from the library shipped with BBTools
  3. Operators built by combining other operators
  4. Custom operators based on algorithms constructed from scratch

A Matlab matrix can be converted to a black-box operator using either bbmatrix or blackbox. Operators, which are shipped with BBTools, can be found in the function reference.

The real power of BBTools comes from its ability to combine the other operators efficiently.


[20] Lloyd Nicholas Trefethen and David Bau III. Numerical Linear Algebra. SIAM, Philadelphia, PA, 1997. ISBN: 0-89871-487-7. (Book)