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IgorKohan committed Apr 10, 2021
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -141,7 +141,7 @@ Spline was evaluated on a uniform Cartesian grid of size 51x51x51. For this case

Further examples are given in documentation.

The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [2]. An idea of the multivariate splines in Sobolev space was initially presented in [8], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [3] and applied for solving a mathematical economics problem in [4]. At the same time an interpolation scheme with Matérn kernels was developed in [9], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [5,6,7].
The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [2]. An idea of the multivariate splines in Sobolev space was initially formulated in [8], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [3] and applied for solving a mathematical economics problem in [4]. At the same time an interpolation scheme with Matérn kernels was developed in [9], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [5,6,7].

## Documentation

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2 changes: 1 addition & 1 deletion docs/src/Normal-Splines-Method.md
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Expand Up @@ -606,7 +606,7 @@ and if the value of this parameter is small enough the normal spline become simi

As well, it is useful to preprocess the source data of the problem by transforming the domain where interpolation nodes are located into the unit hypercube.

The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [8] and [9] and developed in [10]. An idea of the multivariate splines in Sobolev space was initially presented in [25], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [15] and applied for solving a mathematical economics problem in [11]. At the same time an interpolation scheme with Matérn kernels was developed in [26], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [14,21,22].
The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [8] and [9] and developed in [10]. An idea of the multivariate splines in Sobolev space was initially formulated in [25], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [15] and applied for solving a mathematical economics problem in [11]. At the same time an interpolation scheme with Matérn kernels was developed in [26], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [14,21,22].

**References**

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2 changes: 1 addition & 1 deletion docs/src/index.md
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Expand Up @@ -48,7 +48,7 @@ The normal splines method is based on the following functional analysis results:

Using these results it is possible to reduce the task (2) to solving a system of linear equations with symmetric positive definite Gram matrix.

The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [1]. An idea of the multivariate splines in Sobolev space was initially presented in [7], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [2] and applied for solving a mathematical economics problem in [3]. At the same time an interpolation scheme with Matérn kernels was developed in [8], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [4,5,6].
The normal splines method for one-dimensional function interpolation and linear ordinary differential and integral equations was proposed in [1]. An idea of the multivariate splines in Sobolev space was initially formulated in [7], however it was not well-suited to solving real-world problems. Using that idea the multivariate generalization of the normal splines method was developed for two-dimensional problem of low-range computerized tomography in [2] and applied for solving a mathematical economics problem in [3]. At the same time an interpolation scheme with Matérn kernels was developed in [8], this scheme coincides with interpolating normal splines method. Further results related to applications of the normal splines method were reported at the seminars and conferences [4,5,6].

#### References:

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