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Term Paper
Numerical Analysis
MTH 204
Topic: Comparison of rate of convergence of iterative methods
Submitted To: Ramanjeet Kaur
Submitted By: Angad Singh
Roll no: 37
Section: B1801
Regd No: 10801352
Content
Acknowledgement.
Iterative method.
Rate of convergence.
Different Iterative methods.
Rate of convergence of different iterative methods.
Comparison of rate of convergence of iterative methods.
Bibliography.
Acknowledgment
I “Angad Singh” having registration No 10801352 has successfully completed my term paper. I thank our teacher Ms Ramanjeet Kaur for providing this term paper and helping in clearing doubts. I also want to thank the esteemed library of the University for providing the interesting material regarding this topic. I also thank my parents and my friends for being there for me always and for providing moral support.
Terminology
Iterative method:
The term ``iterative method'' refers to a wide range of techniques that use successive approximations to obtain more accurate solutions to a linear system at each step.
Rate of convergence:
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence. Although strictly speaking, a limit does not give information about any finite first part of the sequence, this concept is of practical importance if we deal with a sequence of successive approximations for an iterative method, as then typically fewer iterations are needed to yield a useful approximation if the rate of convergence is higher. This may even make the difference between needing ten or a million iterations.
Iterative methods
Regular-falsi method:
Like the bisection method, the false position method starts with two points a0 and b0 such that f(a0) and f(b0) are of opposite signs, which implies by the intermediate value theorem that the function f
Term Paper
Numerical Analysis
MTH 204
Topic: Comparison of rate of convergence of iterative methods
Submitted To: Ramanjeet Kaur
Submitted By: Angad Singh
Roll no: 37
Section: B1801
Regd No: 10801352
Content
Acknowledgement.
Iterative method.
Rate of convergence.
Different Iterative methods.
Rate of convergence of different iterative methods.
Comparison of rate of convergence of iterative methods.
Bibliography.
Acknowledgment
I “Angad Singh” having registration No 10801352 has successfully completed my term paper. I thank our teacher Ms Ramanjeet Kaur for providing this term paper and helping in clearing doubts. I also want to thank the esteemed library of the University for providing the interesting material regarding this topic. I also thank my parents and my friends for being there for me always and for providing moral support.
Terminology
Iterative method:
The term ``iterative method'' refers to a wide range of techniques that use successive approximations to obtain more accurate solutions to a linear system at each step.
Rate of convergence:
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence. Although strictly speaking, a limit does not give information about any finite first part of the sequence, this concept is of practical importance if we deal with a sequence of successive approximations for an iterative method, as then typically fewer iterations are needed to yield a useful approximation if the rate of convergence is higher. This may even make the difference between needing ten or a million iterations.
Iterative methods
Regular-falsi method:
Like the bisection method, the false position method starts with two points a0 and b0 such that f(a0) and f(b0) are of opposite signs, which implies by the intermediate value theorem that the function f