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Why it is advantageous to combine Newton Raphson method and Bisection method to find the root of an algebraic equation of single variable?
An improved root finding scheme is to combine the bisection and Newton-Raphson methods. The bisection method guarantees a root (or singularity) and is used to limit the changes in position estimated by the Newton-Raphson method when the linear assumption is poor. However, Newton-Raphson steps are taken in the nearly linear regime to speed convergence.
In other words, if we know that we have a root bracketed between our two bounding points, we first consider the Newton-Raphson step. If that would predict a next point that is outside of our bracketed range, then we do a bisection step instead by choosing the midpoint of the range to be the next point. We then evaluate the function at the next point and, depending on the sign of that evaluation, replace one of the bounding points with the new point. This keeps the root bracketed, while allowing us to benefit from the speed of Newton-Raphson.
What else can I help you with?
What is a algerbraic expression?
An algebraic expression is a mathematical sentence that includes a variable but does not have an equal sign. for example: 2x is an algebraic expression 2x = 6 is an equation
What is the defference between bisection method and newton method?
there are three variable are to find but in newton only one variable is taken at a time of a single iteration
Is 7x an algebraic expression?
If x is a variable, then yes. If x refers to multiplication, then no.
What is the basic C-V-P equation?
Sales revenue - Variable costs - Fixed costs = Profit
What is accumulator in digital logic?
It is a variable or a component of a variable.
What is the word for an equation that contains a variable?
An algebraic equation.
What is g in math?
it could be a variable in a algebraic equation.
What is an equation that contains a variable?
It is an equation. It could be an algebraic equation, or a trigonometric equation, a differential equation or whatever, but it is still an equation.
How would you get the variable alone in the equation 4y3?
As it appears, there is no equation but an algebraic term.
When subtracting an algebraic equation which comes first a variable or the constant?
It does not matter.
What is a value of the variable that makes an algebraic sentence true?
It is the solution or root of the equation.
When can you say that a number is called a solution in algebraic expression?
An algebraic equation or inequality can have a solution, an algebraic expression cannot. If substituting a number in place of a variable results in the equation or inequality being a true statement, then that number is a solution of the equation or inequality.
Wha is a linear equation?
A linear equation is when each term in the algebraic equation is either a constant or the product has a single variable and a constant.
What is an algerbraic expression?
An algebraic expression is an expression or and equation that contains at least 1 variable
What does 3k plus 16 equals 5k?
It represents an algebraic equation in the variable, k.
What is the meaning of variable in algebraic expression?
Variable is any letter used in an algebraic expression, and can vary (change form) to be any number, and one variable means the same number in any single algebraic expression. Usually algebra is simplifying the expression or equation until you know what the variable is equal to.
An expression that contains at least one variable is called an algebraic expression?
it is a one-step equation
