This function Initializes the orthogonal series so the function value is the number of terms needed to insure the error is no larger than the requested accuracy.

Function Return Value

INITS — Number of terms needed to insure the error is no larger than ETA.   (Output)

Required Arguments

OS — Vector of length NOS containing coefficients in an orthogonal series.   (Input)

NOS — Number of coefficients in OS.   (Input)

ETA — Requested accuracy of the series.   (Input)
Contrary to the usual convention, ETA is a REAL argument to INITDS.

FORTRAN 90 Interface

Generic:                              INITS (OS, NOS, ETA)

Specific:                             The specific interface names are INITS and INITDS.

FORTRAN 77 Interface

Single:                                INITS (OS, NOS, ETA)

Double:                              The double precision function name is INITDS.

Description

Function INITS initializes a Chebyshev series. The function INITS returns the number of terms in the series s of length n needed to insure that the error of the evaluated series is everywhere less than ETA. The number of input terms n must be greater than 1, so that a series of at least one term and an error estimate can be obtained. In addition, ETA should be larger than the absolute value of the last coefficient. If it is not, then all the terms of the series must be used, and no error estimate is available.

Comments

ETA will usually be chosen to be one tenth of machine precision.

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