5.1.3.2. numdifftools.extrapolation.Dea¶
- class Dea(limexp=50)[source]¶
Extrapolate a slowly convergent sequence using repeated Shanks transformations.
Notes
DEA attempts to extrapolate nonlinearly by Shanks transformations to a better estimate of the sequence’s limiting value, thus improving the rate of convergence. The epsilon algorithm of P. Wynn, see [1]_, is used to perform the non-linear Shanks transformations. The routine is a translation of the DQELG function found in the QUADPACK fortran library, see [2]_ and [3]_.
List of major variables:
- LIMEXP: scalar integer
The maximum number of elements the epsilon table data can contain. The epsilon table is stored in the first (LIMEXP+2) entries of EPSTAB.
- EPSTAB: real vector or size (LIMEXP+2+3)
The first LIMEXP+2 elements contains the two lower diagonals of the triangular epsilon table. The elements are numbered starting at the right-hand corner of the
triangle.
- E0,E1,E2,E3: real scalars
The 4 elements on which the computation of a new element in the epsilon table is based.
- NRES: scalar integer
Number of extrapolation results actually generated by the epsilon algorithm in prior calls to the routine.
- NEWELM: scalar integer
Number of elements to be computed in the new diagonal of the epsilon table. The condensed epsilon table is computed. Only those elements needed for the computation of the next diagonal are preserved.
- RES: real scalar
New element in the new diagonal of the epsilon table.
- ERROR: real scalar
An estimate of the absolute error of RES. The routine decides whether RESULT=RES or RESULT=SVALUE by comparing ERROR with abserr from the previous call.
- RES3LA: real vector of size 3
Contains at most the last 3 results.
Methods
__init__([limexp])Attributes
Maximum number of elements the epsilon table data.