Function-valued Padé-type approximant via E-algorithm and its applications in solving integral equations

A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

“…In this section, we will give the definition of the functionvalued Padé-type approximation [15][16][17][18]. Let ( ) : P → C be a linear functional on the polynomial space P, and define it by…”

“…Rational approximation has extensive application in engineering, technology and calculation [12][13][14][15][16][17][18]. As efficient rational approximating techniques, a generalized inverse function-valued Padé approximants had been used in solving integral equation [13,14], and a function-valued Padé-type approximation method was used to solve one and twodimensional Fredholm integral equation of the second kind [15][16][17][18].…”

“…For domain , some works treat the square case [4][5][6][7][8][9][10] and some are based on discrete Galerkin method [5], Monte Carlo methods [6], or piecewise approximating polynomials [7], Nytröm methods based on cubature rules obtained as the tensor product of two-variate Gaussian 2 Mathematical Problems in Engineering rules [8,10], and meshless method with complex factors [11]. Rational approximation has extensive application in engineering, technology and calculation [12][13][14][15][16][17][18]. As efficient rational approximating techniques, a generalized inverse function-valued Padé approximants had been used in solving integral equation [13,14], and a function-valued Padé-type approximation method was used to solve one and twodimensional Fredholm integral equation of the second kind [15][16][17][18].…”