Kazem Nouri

Convergence of numerical solution of the Fredholm integral equation of the first kind with degenerate kernel

Fredholm integral equation of the first kind is one of the ill posed problems since in the operator form of integral equation the integral operator does not have bounded inverse. In this article we consider integral equation of the first kind with degenerate kernel which has bounded inverse. We use collocation method by wavelet families for numerical solving of the equation. Then we prove the convergence for the numerical method. We use conjugate gradiant method for solving the system of linear equations after discretizing the integral equation. For showing efficiency of the method some examples are used.

Discussion on convergence of Legendre polynomial for numerical solution of integral equations

In this article, a numerical solution of Fredholm integral equation of the second kind will be discussed, for this result, we choose Legendre polynomials as basis functions and collocation method to estimate a solution for an unknown function in this equation. Convergence of this method and rate of convergence will be investigated. Finally, some numerical examples will be stated to show the accuracy of this method.

Computational methods for integrals involving functions and Daubechies wavelets

Abstract When wavelets are used as basis functions in Galerkin approach to solve the integral equations, Integrals of the form ∫ supp ( θ j , k ) f ( x ) θ j , k ( x ) d x occur. By a change of variable, these integrals can be translated into integrals involving only θ. In this paper, we find quadrature rule on the supp ( θ ) for the integrals of the form ∫ supp ( θ ) f ( x ) θ ( x ) d x , θ ∈ { ϕ , ψ } . Wavelets in this article are those discovered by Daubechies [I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988) 909–996], where ϕ is the scaling function and ψ is the wavelet function.

Wavelet-based gender detection on off-line handwritten documents using probabilistic finite state automata

Detection of gender from handwriting of an individual presents an interesting research problem with applications in forensic document examination, writer identification and psychological studies. This paper presents an effective technique to predict the gender of an individual from off-line images of handwriting. The proposed technique relies on a global approach that considers writing images as textures. Each handwritten image is converted into a textur\ed image which is decomposed into a series of wavelet sub-bands at a number of levels. The wavelet sub-bands are then extended into data sequences. Each data sequence is quantized to produce a probabilistic finite state automata (PFSA) that generates feature vectors. These features are used to train two classifiers, artificial neural network and support vector machine to discriminate between male and female writings. The performance of the proposed system was evaluated on two databases, QUWI and MSHD, within a number of challenging experimental scenarios and realized classification rates of up to 80%. The experimental results show the superiority of the proposed technique over existing techniques in terms of classification rates. Prediction of gender from offline images of handwriting using textural informationWavelet transform using symbolic dynamic filtering for feature extractionClassification using support vector machine and artificial neural networksScript-independent approach applied to English, French & Arabic handwritingsImproved results on the QUWI & MSHD databases once compared to existing methods

Numerical solution of Volterra–Fredholm integral equations using the collocation method based on a special form of the Müntz–Legendre polynomials

Abstract This paper presents a computational technique based on a special family of the Muntz–Legendre polynomials to solve a class of Volterra–Fredholm integral equations. The relationship between the Jacobi polynomials and Muntz–Legendre polynomials, in a particular state, are expressed. The proposed method reduces the integral equation into algebraic equations via the Chebyshev–Gauss–Lobatto points, so that the system matrix coefficients are obtained by the least squares approximation method. The useful properties of the Jacobi polynomials are exploited to analyze the approximation error. The performance and accuracy of our method are examined with some illustrative examples.

A Novel Database for Automatic Processing of Persian Handwritten Bank Checks

Abstract This paper introduces a database of Persian handwritten bank checks. The database includes legal amounts, courtesy amounts, dates, receiver names, signatures and account numbers. In addition to checks, the database also comprises handwritten forms with words used in legal amounts, digits employed in the courtesy amounts and signatures of contributors. The database can be employed for evaluation of segmentation and recognition of different fields in checks as well as for verification of signatures. Data is collected and organized in two series. The first series, comprising 500 hand filled Persian checks and 500 forms contributed by 500 different individuals, supports evaluation of segmentation and recognition tasks. The second series contributed by 100 writers supports evaluation of signature verification systems and comprises 200 genuine checks, 100 forms and 200 forged checks. To provide an insight to other researchers, experiments have been carried out on recognition of dates and courtesy amounts with recognition rates of 76% and 73%, respectively. Likewise, experiments on signature verification with skilled forgeries realized an average error rate of 12.25%. The database, named Persian Handwriting Bank Checks (PHBC) Database, is freely available to the research community upon request to the authors. It is expected that the developed database will not only allow researchers working on automatic processing of Persian checks to evaluate their proposed techniques but will also serve to meaningfully compare different recognition and verification techniques.

Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay

In this paper, by means of the Banach fixed point theorem and the Krasnoselskiis fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

Implementation of the modified Monte Carlo simulation for evaluate the barrier option prices

Abstract In this paper, we apply an improved version of Monte Carlo methods to pricing barrier options. This kind of options may match with risk hedging needs more closely than standard options. Barrier options behave like a plain vanilla option with one exception. A zero payoff may occur before expiry, if the option ceases to exist; accordingly, barrier options are cheaper than similar standard vanilla options. We apply a new Monte Carlo method to compute the prices of single and double barrier options written on stocks. The basic idea of the new method is to use uniformly distributed random numbers and an exit probability in order to perform a robust estimation of the first time the stock price hits the barrier. Using uniformly distributed random numbers decreases the estimation of first hitting time error in comparison with standard Monte Carlo or similar methods. It is numerically shown that the answer of our method is closer to the exact value and the first hitting time error is reduced.

A New Database for Writer Demographics Attributes Detection Based on Off-Line Persian and English Handwriting

This paper describes a database of multi-script (Persian and English) for typical and new aspects and challenges of offline handwriting automatic analysis field. This database can be used for typical aspects such as different levels of segmentation and recognition and writer identification in text-dependent and text-independent modes. Also, new aspects can be used such as writer identification and gender, age and handedness detection based on script-dependent and script-independent. Two pages of forms in three regions were designed and collected from 200 native Persian writers of different age, handednesses, genders and education level. To the best of our knowledge, so far no attempt has been conducted on providing Persian database for writer identification and gender, age and handedness detection based on script-dependent and script-independent in multi-script environment.

An efficient method for solving system of Volterra integral equations

Purpose – The purpose of this paper is to discuss a numerical method for solving system of Volterra integral equations.Design/methodology/approach – An expansion method known as Chebyshev collocation method is chosen to convert the system of integral equations to the linear algebraic system of equations, so by solving the linear algebraic system an approximate solution is concluded.Findings – Some numerical results support the accuracy and efficiency of the stated method.Originality/value – The paper presents a method for solving first and second kind system of integral equations.