Asset Details
Do you wish to reserve the book?
Computation of incomplete beta function ratios Ix(a,b) with Deuflhard’s algorithm
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Computation of incomplete beta function ratios Ix(a,b) with Deuflhard’s algorithm
Do you wish to request the book?
Computation of incomplete beta function ratios Ix(a,b) with Deuflhard’s algorithm
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Computation of incomplete beta function ratios Ix(a,b) with Deuflhard’s algorithm
2024
Overview
Gautschi proposed a method for computing incomplete beta functions
I
x
(
a
,
b
)
using Miller’s algorithm with a three-term recurrence relation and showed a computation program in ALGOL. In this paper, first, Miller’s algorithm using the recurrence relation satisfied by
f
k
(
x
)
=
I
x
(
a
+
k
,
b
)
is described. Next, another solution that is first-order independent of
f
k
(
x
)
of the recurrence relation is given, and its general solution can be expressed as a linear sum of these. Using this general solution, an error analysis for the function
I
x
(
a
,
b
)
is performed for the first time. The relative error of the function values is then expressed in a new formula to a trend of the error behavior. Also, Miller’s algorithm with a normalizing sum is explained and its error analysis is performed. Since Miller’s algorithm requires a predefined number of iterations of the recurrence relation, it is necessary to repeat the computation of the recurrence relation with increasing number of iterations until the required accuracy will be met. Therefore, in this paper, we apply Deuflhard’s algorithm, which can automatically obtain the function value with the required accuracy. This algorithm requires far fewer iterations than Gautschi’s algorithm to obtain the same accuracy.
Publisher
Springer US,Springer Nature B.V
Subject
