Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2016, Volume 439, Issue 1, pp. 32 - 56

...., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application...

Exponential B-spline | Exponential polynomial reproduction | Nonstationary subdivision | Minimal support | Exponential pseudo-spline | NONSTATIONARY SUBDIVISION SCHEMES | MATHEMATICS | MATHEMATICS, APPLIED | POLYNOMIAL REPRODUCTION | FRAMEWORK | FINITE-ELEMENT-ANALYSIS

Exponential B-spline | Exponential polynomial reproduction | Nonstationary subdivision | Minimal support | Exponential pseudo-spline | NONSTATIONARY SUBDIVISION SCHEMES | MATHEMATICS | MATHEMATICS, APPLIED | POLYNOMIAL REPRODUCTION | FRAMEWORK | FINITE-ELEMENT-ANALYSIS

Journal Article

Applied and Computational Harmonic Analysis, ISSN 1063-5203, 09/2018, Volume 45, Issue 2, pp. 341 - 358

We introduce a universal and systematic way of defining a generalized B-spline based on a linear shift-invariant (LSI) operator L (a.k.a. Fourier multiplier...

Differential operator | Discrete approximation | Transfer function | Spline | MATHEMATICS, APPLIED | EXPONENTIAL SPLINES

Differential operator | Discrete approximation | Transfer function | Spline | MATHEMATICS, APPLIED | EXPONENTIAL SPLINES

Journal Article

3.
Full Text
Exponential B-splines Galerkin Method for the Numerical Solution of the Fisher’s Equation

Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, 12/2018, Volume 42, Issue 4, pp. 2189 - 2198

A finite element solution of the Fisher’s equation based on the Galerkin method whose weight and shape functions are exponential B-splines are constructed...

Materials Science, general | Earth Sciences, general | 35K57 | Exponential B-splines | Fisher’s equation | Engineering | Life Sciences, general | Chemistry/Food Science, general | Galerkin method | 65M60 | Engineering, general | Physics, general | 41A15 | TRAVELING-WAVE SOLUTIONS | COLLOCATION METHOD | MULTIDISCIPLINARY SCIENCES | Fisher's equation | ALGORITHM | DIFFUSION | Finite element method | Wave propagation | Splines | Diffusion effects | Traveling waves | Weight | Shape functions

Materials Science, general | Earth Sciences, general | 35K57 | Exponential B-splines | Fisher’s equation | Engineering | Life Sciences, general | Chemistry/Food Science, general | Galerkin method | 65M60 | Engineering, general | Physics, general | 41A15 | TRAVELING-WAVE SOLUTIONS | COLLOCATION METHOD | MULTIDISCIPLINARY SCIENCES | Fisher's equation | ALGORITHM | DIFFUSION | Finite element method | Wave propagation | Splines | Diffusion effects | Traveling waves | Weight | Shape functions

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 10/2012, Volume 37, Issue 3, pp. 301 - 318

We provide an explicit formula for a large class of exponential B-splines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant...

Frames | Algebra | Calculus of Variations and Optimal Control; Optimization | Computer Science | Numeric Computing | Mathematics, general | Theory of Computation | Dual frames | 42C15 | Exponential B-splines | INTERPOLATION | MATHEMATICS, APPLIED | ALGORITHMS

Frames | Algebra | Calculus of Variations and Optimal Control; Optimization | Computer Science | Numeric Computing | Mathematics, general | Theory of Computation | Dual frames | 42C15 | Exponential B-splines | INTERPOLATION | MATHEMATICS, APPLIED | ALGORITHMS

Journal Article

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Zak transforms and Gabor frames of totally positive functions and exponential B-splines

Journal of Approximation Theory, ISSN 0021-9045, 08/2014, Volume 184, pp. 209 - 237

We study totally positive (TP) functions of finite type and exponential B-splines as window functions for Gabor frames...

Exponential B-spline | Gabor frame | Zak transform | Total positivity | MATHEMATICS

Exponential B-spline | Gabor frame | Zak transform | Total positivity | MATHEMATICS

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2008, Volume 219, Issue 2, pp. 509 - 517

.... We present an alternative algorithm for their computation, based on the representation of HPF in terms of integral remainders with B-splines as Peano kernels...

Computation of the exponential | Hermite-Padé approximation | MATHEMATICS, APPLIED | COMPUTATION | Hermite-Pade approximation | computation of the exponential | Algorithms | Numerical Analysis | Mathematics

Computation of the exponential | Hermite-Padé approximation | MATHEMATICS, APPLIED | COMPUTATION | Hermite-Pade approximation | computation of the exponential | Algorithms | Numerical Analysis | Mathematics

Journal Article

Dolomites Research Notes on Approximation, 2017, Volume 10, pp. 31 - 42

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 4/2013, Volume 38, Issue 3, pp. 647 - 666

.... Based on these results, we see that the exponential B-spline generates exponential polynomials in the associated spaces, but it may not reproduce any exponential polynomials...

Non-stationary subdivision scheme | Algebra | Calculus of Variations and Optimal Control; Optimization | Approximation order | Computer Science | Numeric Computing | Exponential polynomial reproduction | Exponential B-spline | Mathematics, general | Theory of Computation | Normalization | INTERPOLATION | TENSION CONTROL | MATHEMATICS, APPLIED | MESHES | SURFACES | Functions, Exponential | Polynomials | Research | Spline theory | Subdivisions | Conics | Approximation | Computation | Mathematical analysis | Mathematical models | Flexibility

Non-stationary subdivision scheme | Algebra | Calculus of Variations and Optimal Control; Optimization | Approximation order | Computer Science | Numeric Computing | Exponential polynomial reproduction | Exponential B-spline | Mathematics, general | Theory of Computation | Normalization | INTERPOLATION | TENSION CONTROL | MATHEMATICS, APPLIED | MESHES | SURFACES | Functions, Exponential | Polynomials | Research | Spline theory | Subdivisions | Conics | Approximation | Computation | Mathematical analysis | Mathematical models | Flexibility

Journal Article

Calcolo, ISSN 0008-0624, 12/2014, Volume 51, Issue 4, pp. 599 - 613

We derive explicit formulas for the generating functions of B-splines with knots in either geometric or affine progression...

Knots in affine progression | 05A30 | Numerical Analysis | Generating functions | q$$ q -Exponentials | 65D17 | Mathematics | Theory of Computation | Knots in geometric progression | q$$ q -Derivatives | 65D07 | B-splines | q-Exponentials | q-Derivatives | MATHEMATICS | MATHEMATICS, APPLIED | Computer science | Geometry | Mathematical functions | Progressions | Construction | Nonuniform | Partial differential equations | Texts | Derivatives | Knots | Sums

Knots in affine progression | 05A30 | Numerical Analysis | Generating functions | q$$ q -Exponentials | 65D17 | Mathematics | Theory of Computation | Knots in geometric progression | q$$ q -Derivatives | 65D07 | B-splines | q-Exponentials | q-Derivatives | MATHEMATICS | MATHEMATICS, APPLIED | Computer science | Geometry | Mathematical functions | Progressions | Construction | Nonuniform | Partial differential equations | Texts | Derivatives | Knots | Sums

Journal Article

Nonlinear Engineering, ISSN 2192-8010, 06/2018, Volume 7, Issue 2, pp. 113 - 125

...) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis...

mExp-DQM | 35L04 | 74Sxx | hyperbolic telegraph equation | Thomas algorithm | 35L10 | Differential quadrature method | modified exponential cubic B-splines | Algorithms | Splines | Numerical methods | Differential equations | Eigenvalues | Norms | Ordinary differential equations | Time integration

mExp-DQM | 35L04 | 74Sxx | hyperbolic telegraph equation | Thomas algorithm | 35L10 | Differential quadrature method | modified exponential cubic B-splines | Algorithms | Splines | Numerical methods | Differential equations | Eigenvalues | Norms | Ordinary differential equations | Time integration

Journal Article

Abstract and applied analysis, ISSN 1085-3375, 11/2011, Volume 2011, pp. 1 - 17

This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines...

MATHEMATICS | SUBDIVISION SCHEMES | ALGORITHMS | MULTIRESOLUTION ANALYSIS | LINEAR INDEPENDENCE | CONSTRUCTION | Wavelet transforms | Functions, Exponential | Research | Spline theory

MATHEMATICS | SUBDIVISION SCHEMES | ALGORITHMS | MULTIRESOLUTION ANALYSIS | LINEAR INDEPENDENCE | CONSTRUCTION | Wavelet transforms | Functions, Exponential | Research | Spline theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 272, pp. 53 - 63

.... They can be seen as a generalization and extension of the Keys interpolation kernel using cardinal exponential B-splines...

Compact support | Interpolation | Parametric surfaces | Parametric curves | Exponential B-splines | B-splines | MATHEMATICS, APPLIED | DESIGN | CARDINAL EXPONENTIAL SPLINES | CONSTRUCTION | SUBDIVISION SCHEMES

Compact support | Interpolation | Parametric surfaces | Parametric curves | Exponential B-splines | B-splines | MATHEMATICS, APPLIED | DESIGN | CARDINAL EXPONENTIAL SPLINES | CONSTRUCTION | SUBDIVISION SCHEMES

Journal Article

Statistical Papers, ISSN 0932-5026, 8/2019, Volume 60, Issue 4, pp. 1119 - 1135

We establish an identity that relates B-spline functions to linear combinations of gamma density functions...

Generalized Type-I progressive hybrid censoring | Statistics for Business, Management, Economics, Finance, Insurance | Divided differences | Exponential distribution | Progressive censoring | Economic Theory/Quantitative Economics/Mathematical Methods | Probability Theory and Stochastic Processes | Type-I censored sequential k -out-of- n systems | Statistics | Simple step-stress model | Generalized Type-II progressive hybrid censoring | Gamma distribution | Hybrid censoring | Type-II progressive hybrid censoring | Operations Research/Decision Theory | Type-I progressive hybrid censoring | B-spline | Adaptive Type-I progressive hybrid censoring | Type-I censored sequential k-out-of-n systems | STATISTICS & PROBABILITY | EXACT LIKELIHOOD INFERENCE | DISTRIBUTIONS | STEP-STRESS MODEL | EXPONENTIAL-DISTRIBUTION | PARAMETER | Censorship | Density | B spline functions | Representations

Generalized Type-I progressive hybrid censoring | Statistics for Business, Management, Economics, Finance, Insurance | Divided differences | Exponential distribution | Progressive censoring | Economic Theory/Quantitative Economics/Mathematical Methods | Probability Theory and Stochastic Processes | Type-I censored sequential k -out-of- n systems | Statistics | Simple step-stress model | Generalized Type-II progressive hybrid censoring | Gamma distribution | Hybrid censoring | Type-II progressive hybrid censoring | Operations Research/Decision Theory | Type-I progressive hybrid censoring | B-spline | Adaptive Type-I progressive hybrid censoring | Type-I censored sequential k-out-of-n systems | STATISTICS & PROBABILITY | EXACT LIKELIHOOD INFERENCE | DISTRIBUTIONS | STEP-STRESS MODEL | EXPONENTIAL-DISTRIBUTION | PARAMETER | Censorship | Density | B spline functions | Representations

Journal Article

Biometrika, ISSN 0006-3444, 01/2015, Volume 103, Issue 1, pp. 121 - 131

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and...

Equivalent kernel | Euler-Frobenius polynomial | Exponential spline | B-spline | Demmler-Reinsch basis | SMOOTHING NOISY DATA | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | PENALIZED SPLINES | STATISTICS & PROBABILITY | ASYMPTOTICS | KERNELS

Equivalent kernel | Euler-Frobenius polynomial | Exponential spline | B-spline | Demmler-Reinsch basis | SMOOTHING NOISY DATA | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | PENALIZED SPLINES | STATISTICS & PROBABILITY | ASYMPTOTICS | KERNELS

Journal Article

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Exponential B-Splines for Numerical Solutions to Some Boussinesq Systems for Water Waves

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2016, Volume 13, Issue 6, pp. 4975 - 4994

In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one-dimensional Boussinesq systems numerically...

collocation | solitary waves | 65M70 | 76B25 | 35Q99 | Mathematics, general | Mathematics | Boussinesq systems | wave generation | 65D07 | exponential cubic B-spline | 35C07 | MATHEMATICS | MATHEMATICS, APPLIED | COLLOCATION METHOD | EQUATIONS | Water waves

collocation | solitary waves | 65M70 | 76B25 | 35Q99 | Mathematics, general | Mathematics | Boussinesq systems | wave generation | 65D07 | exponential cubic B-spline | 35C07 | MATHEMATICS | MATHEMATICS, APPLIED | COLLOCATION METHOD | EQUATIONS | Water waves

Journal Article

Journal of Abstract and Computational Mathematics, ISSN 2149-7168, 05/2018, Volume 3, Issue 2, pp. 01 - 10

The goal of the present paper is to present numerical treatments for solving matrix differential equations of second order using exponential and trigonometric cubic B-splines...

trigonometric cubic B-spline | kronecker product | Matrix differential equations | frobenius norm | exponential cubic B-spline

trigonometric cubic B-spline | kronecker product | Matrix differential equations | frobenius norm | exponential cubic B-spline

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 05/2014, Volume 60, Issue 5, pp. 3036 - 3051

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of...

White noise | Technological innovation | Polynomials | Mathematical model | Splines (mathematics) | Stochastic processes | innovation modeling | non-Gaussian stochastic processes | Sparsity | infinite divisibility | Lévy process | CARMA processes | sampling | continuous-time signals | stochastic differential equations | exponential B-splines | COMPUTER SCIENCE, INFORMATION SYSTEMS | DRIVEN | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | CARDINAL EXPONENTIAL SPLINES | Levy process | Technology application | Usage | Analysis | Gaussian processes | Distribution (Probability theory) | Spline theory | Methods | Poles | Correlation | Mathematical analysis | Mathematical models | Probability distribution | Gaussian | Stochasticity | Information theory

White noise | Technological innovation | Polynomials | Mathematical model | Splines (mathematics) | Stochastic processes | innovation modeling | non-Gaussian stochastic processes | Sparsity | infinite divisibility | Lévy process | CARMA processes | sampling | continuous-time signals | stochastic differential equations | exponential B-splines | COMPUTER SCIENCE, INFORMATION SYSTEMS | DRIVEN | ENGINEERING, ELECTRICAL & ELECTRONIC | MODELS | CARDINAL EXPONENTIAL SPLINES | Levy process | Technology application | Usage | Analysis | Gaussian processes | Distribution (Probability theory) | Spline theory | Methods | Poles | Correlation | Mathematical analysis | Mathematical models | Probability distribution | Gaussian | Stochasticity | Information theory

Journal Article

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, ISSN 0340-6253, 2017, Volume 77, Issue 2, pp. 507 - 526

.... The sinc differential quadrature combined with third-fourth order implicit Rosenbrock and exponential B-spline collocation methods are setup to obtain the numerical solutions of the mentioned problems...

DIFFERENTIAL QUADRATURE | SELF-REPLICATING SPOTS | GALERKIN METHOD | BOUNDARY-VALUE-PROBLEMS | REACTION-DIFFUSION SYSTEM | EXPONENTIAL B-SPLINES | CHEMISTRY, MULTIDISCIPLINARY | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SINC-COLLOCATION METHOD | FISHERS EQUATION | OSCILLATIONS

DIFFERENTIAL QUADRATURE | SELF-REPLICATING SPOTS | GALERKIN METHOD | BOUNDARY-VALUE-PROBLEMS | REACTION-DIFFUSION SYSTEM | EXPONENTIAL B-SPLINES | CHEMISTRY, MULTIDISCIPLINARY | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SINC-COLLOCATION METHOD | FISHERS EQUATION | OSCILLATIONS

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 03/2015, Volume 1648

Conference Proceeding

IEICE transactions on fundamentals of electronics, communications and computer sciences, ISSN 0916-8508, 06/2002, Volume 85, Issue 6, pp. 1265 - 1273

This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals...

Reconstruction | Decomposition | Exponential spline | B-spline | INTERPOLATION | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | exponential spline | COMPUTER SCIENCE, INFORMATION SYSTEMS | reconstruction | decomposition | ENGINEERING, ELECTRICAL & ELECTRONIC

Reconstruction | Decomposition | Exponential spline | B-spline | INTERPOLATION | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | exponential spline | COMPUTER SCIENCE, INFORMATION SYSTEMS | reconstruction | decomposition | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

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