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Book ChapterDOI

Triangular Orthogonal Functions for the Analysis of Continuous Time Systems: Walsh, Block Pulse, and Related Orthogonal Functions in Systems and Control

About: The article was published on 2011-05-01. It has received 18 citations till now. The article focuses on the topics: Walsh function & Walsh matrix.
Citations
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Journal ArticleDOI
TL;DR: A numerical method based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of nonlinear Volterra-Fredholm integral equations.

79 citations

Journal ArticleDOI
TL;DR: This paper presented an approximate method for solving optimal control problem of Volterra integral equations based upon orthogonal triangular functions that has been proved for optimal control and cost functionals.

30 citations

Journal ArticleDOI
TL;DR: An efficient expansion-iterative method based on the block-pulse functions is proposed for numerically solving Volterra integral equation of the first kind, and the approximate solution is most easily produced iteratively via the recurrence relation.
Abstract: Most integral equations of the first kind are ill-posed, and obtaining their numerical solution often leads to solving a linear system of algebraic equations of a large condition number. So, solving this system is difficult or impossible. For numerically solving Volterra integral equation of the first kind an efficient expansion-iterative method based on the block-pulse functions is proposed. Using this method, solving the first kind integral equation reduces to solving a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to solve any linear system of algebraic equations. To show the convergence and stability of the method, some computable error bounds are obtained. Numerical examples are provided to illustrate that the method is practical and has good accuracy.

23 citations

Journal ArticleDOI
TL;DR: A new set of hybrid functions (HF) which evolved from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) is proposed which is employed for solving identification problem from impulse response data.

23 citations

Journal ArticleDOI
TL;DR: In this article, a numerical method based on orthogonal triangular functions (TFs) is proposed to approximate the solution of Fredholm integral equations systems, which does not need any integration for obtaining the constant coefficients and can be applied in a simple and fast technique.

21 citations


Cites background from "Triangular Orthogonal Functions for..."

  • ...Multiplication of triangular functions and related properties were first treated in [9]....

    [...]

  • ...for both Fredholm and Volterra integral equations of the second kind in [9]....

    [...]

  • ...,m 1 and h 1⁄4 T m [8,9]....

    [...]

References
More filters
Journal ArticleDOI
TL;DR: A numerical method based on an m-set of general, orthogonal triangular functions (TF) is proposed to approximate the solution of nonlinear Volterra-Fredholm integral equations.

79 citations

Journal ArticleDOI
TL;DR: This paper presented an approximate method for solving optimal control problem of Volterra integral equations based upon orthogonal triangular functions that has been proved for optimal control and cost functionals.

30 citations

Journal ArticleDOI
TL;DR: An efficient expansion-iterative method based on the block-pulse functions is proposed for numerically solving Volterra integral equation of the first kind, and the approximate solution is most easily produced iteratively via the recurrence relation.
Abstract: Most integral equations of the first kind are ill-posed, and obtaining their numerical solution often leads to solving a linear system of algebraic equations of a large condition number. So, solving this system is difficult or impossible. For numerically solving Volterra integral equation of the first kind an efficient expansion-iterative method based on the block-pulse functions is proposed. Using this method, solving the first kind integral equation reduces to solving a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to solve any linear system of algebraic equations. To show the convergence and stability of the method, some computable error bounds are obtained. Numerical examples are provided to illustrate that the method is practical and has good accuracy.

23 citations

Journal ArticleDOI
TL;DR: A new set of hybrid functions (HF) which evolved from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) is proposed which is employed for solving identification problem from impulse response data.

23 citations

Journal ArticleDOI
TL;DR: In this article, a numerical method based on orthogonal triangular functions (TFs) is proposed to approximate the solution of Fredholm integral equations systems, which does not need any integration for obtaining the constant coefficients and can be applied in a simple and fast technique.

21 citations