Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Find_root_abs Calculator

Find_root_abs

-- Option variable: find_root_abs -- Option variable: find_root_rel Finds a root of the expression <expr> or the function <f> over the closed interval [<a>, <b>]. The expression <expr> may be an equation, in which case find_root seeks a root of lhs(<expr>) - rhs(<expr>).

Given that Maxima can evaluate <expr> or <f> over [<a>, <b>] and that <expr> or <f> is continuous, find_root is guaranteed to find the root, or one of the roots if there is more than one.

find_root initially applies binary search. If the function in question appears to be smooth enough, find_root applies linear interpolation instead.

The accuracy of find_root is governed by find_root_abs and find_root_rel. find_root stops when the function in question evaluates to something less than or equal to find_root_abs, or if successive approximants <x_0>, <x_1> differ by no more than find_root_rel * max(abs(x_0), abs(x_1)). The default values of find_root_abs and find_root_rel are both zero.

find_root expects the function in question to have a different sign at the endpoints of the search interval. When the function evaluates to a number at both endpoints and these numbers have the same sign, the behavior of find_root is governed by find_root_error. When find_root_error is true, find_root prints an error message. Otherwise find_root returns the value of find_root_error. The default value of find_root_error is true.

If <f> evaluates to something other than a number at any step in the search algorithm, find_root returns a partially-evaluated find_root expression.

The order of <a> and <b> is ignored; the region in which a root is sought is [min(<a>, <b>), max(<a>, <b>)].

Examples:

          (%i1) f(x) := sin(x) - x/2;
                                                  x
          (%o1)                  f(x) := sin(x) - -
                                                  2
          (%i2) find_root (sin(x) - x/2, x, 0.1, %pi);
          (%o2)                   1.895494267033981
          (%i3) find_root (sin(x) = x/2, x, 0.1, %pi);
          (%o3)                   1.895494267033981
          (%i4) find_root (f(x), x, 0.1, %pi);
          (%o4)                   1.895494267033981
          (%i5) find_root (f, 0.1, %pi);
          (%o5)                   1.895494267033981
          (%i6) find_root (exp(x) = y, x, 0, 100);
                                      x
          (%o6)           find_root(%e  = y, x, 0.0, 100.0)
          (%i7) find_root (exp(x) = y, x, 0, 100), y = 10;
          (%o7)                   2.302585092994046
          (%i8) log (10.0);
          (%o8)                   2.302585092994046

(%o1)                                true
(%i2) 

Find_root_abs Example

Related Examples

abs

g(c):=2*c^3 - 11.7*c^...

f(x,y):=x-((g(x)*(y-x...

f(4,3);

Calculate

abs-log

v_e=(r_a-r_h)/8;

v_a=s_a-((s_a-s_h)/2);

d=v_a-v_e;

Calculate

abs-do-expintegral_ei-float-log-makelist-print-sum

a1(x) := float(0.5772...

a2(x) := float(%e ^ x...

a3(x) := float(%e ^ x...

Calculate

abs-define

define(f(x), (x^4 + 3...

define(g(x), abs(4*x/...

find_roots(g(x)=2);

Calculate

abs-acos-cos-sin

sgn(x):=if x>0 the...

f1(n,h):= abs( cos( %...

f2(s,h):= acos( s)*h ...

Calculate

abs-erf-exp-plot2d-sqrt
plot2d([f(t),f1(t),f2(t),f3(t)],[t,-5,5]);

b:4;

f(t):= 1/(1+exp(-b*t));

f1(t):=erf(t);

Calculate

abs-define-float-realroots

define(f(x), (x^4+3*x...

define(g(x), abs(4*x/...

float(f(3.2));

Calculate

abs-define-diff-expand-find_root-float-plot2d-realroots
plot2d([g(x),z(x)],[x,-5,5],[y,0,5]);

define(f(x),(x^4+3*x^...

define(g(x),abs(4*x)/...

f(3.2);

Calculate

abs-grind-numer-sqrt

N(x) := x/2+1/x;

x: 17/12;

N(x);

Calculate