BBTools

bbinv

This function is not yet fully documented. This is a transcript of the text-formatted help.

bbinv  Create a black-box operator for an inverse matrix
   BB=bbinv(A) creates a black-box operator for the inverse of a matrix
   A. Thus, BB*X and A\X are roughly equivalent, except that BB contains
   a precomputed factorization suitable for mass evaluation.

   bbinv computes a factorization, which is used to solve the
   linear system. The factorization may be specified as a parameter:
     'auto'    - Automatic (default)
     'QR'      - QR
     'QRP'     - QR with column pivoting
     'chol'    - Cholesky factorization (same as 'SPD')
     'LUP'     - LU with partial pivoting (same as 'GEPP' and 'LU')
     'LUPQ'    - LU with column and row pivoting (sparse only)
     'svd'     - Singular Value Decomposition
     'inv'     - Form an explicit inverse
   The following systems are supported without factorization:
     'D'       - Diagonal
     'L'       - Lower triangular
     'U'       - Upper triangular
   The following options must be followed by a scalar:
     'inorm'   - Lower bound for norm(inv(A))
     'thresh'  - Threshold passed to LU
   In addition, the following flag may be specified:
     'notol'   - Do not compute tolerances

   Several methods may be specified. The method will be the first
   applicable method in this list ('auto' specifies the first 6 methods):
     D, L, U, chol, LUPQ, QRP, QR, LUP, LU, svd, and inv.

   bbinv works hard to determine the accuracy of the operator. This step
   is skipped if 'notol' is given as parameter. This may increase the
   speed of creating the operator, but some iterative methods may not
   function. Specifying 'inorm' directly may also speed up this process,
   although this is almost useless for LU-factorizations.

   Note: Y=BB*X satisfy (A+E)*Y=X where E is a perturbation. While E is a
   important for interpreting Y, the most important issue for iterative
   algorithms is linearity. For dense systems, 'QRP' is a good compromise
   between accuracy and efficiency.

   See also QR, LU, , , .

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