Skip to Main Content
Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Solution of Algebraic and Transcendental Equations 5-13
0
10
0
()
()
fx
xx
fx
⇒=−
(5.11)
From this we write the Newton–Raphson
iteration formula
1
()
()
n
nn
n
fx
xx
fx
+
=−
(5.12)
This formula can also be obtained using Taylor
series expansion of f at x = x
0
:
2
0
000 0
()
() ()( )() ()
2!
xx
fx fx x x f x f x
=+− + +
′′′
(5.13)
For a first approximation x
1
of x we truncate the
series and obtain a linear equation
10100
0
10
0
() ()( )()0
()
()
fx fx x x f x
fx
xx
fx
=+− =
⇒=−
(5.14)
From this we obtain iteration formula (5.12).
Newton–Raphson method for solving
equation f (x) = 0
Algorithm NEWTON ( f, f ¢, x
0
, Œ, N)
This algorithm computes a solution of f ( x) = 0 given
an initial ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Mathematical Methods by Pearson

Applied Mathematical Methods by Pearson

Bhaskar Dasgupta
Mathematical Modelling

Mathematical Modelling

Pramod Belkhode, Prashant Maheshwary, Kanchan Borkar, J.P. Modak

Publisher Resources

ISBN: 9781299446557Publisher Website