Climate of the past, ISSN 1814-9332, 2018, Volume 14, Issue 6, pp. 709 - 724

Here we present the results of the inversion of a multi-annual temperature profile (2013, 2014, 2015) of the deepest borehole (235 m) in the mountain...

ICE-AGE | VARIABILITY | GLACIER | IMPACT | GEOSCIENCES, MULTIDISCIPLINARY | EUROPEAN ALPS | THERMAL REGIME | MILLENNIUM | HOLOCENE | METEOROLOGY & ATMOSPHERIC SCIENCES | SNOW COVER | CLIMATE | Thermal properties | Frozen ground | Soils | Models | Borings | Soil temperature | Latent heat | Glaciation | Temperature | Boreholes | Inversion | Surface temperature | Permafrost | Temperature profiles | Little Ice Age | Dolostone | Annual | Permafrost temperatures | Temperature effects | Air temperature | Thermistors | Mathematical models | Porosity | Regularization | Drilling | Ice ages | Laboratories | Heat conductivity | Mountains | Thermodynamics | Accuracy | High temperature effects

ICE-AGE | VARIABILITY | GLACIER | IMPACT | GEOSCIENCES, MULTIDISCIPLINARY | EUROPEAN ALPS | THERMAL REGIME | MILLENNIUM | HOLOCENE | METEOROLOGY & ATMOSPHERIC SCIENCES | SNOW COVER | CLIMATE | Thermal properties | Frozen ground | Soils | Models | Borings | Soil temperature | Latent heat | Glaciation | Temperature | Boreholes | Inversion | Surface temperature | Permafrost | Temperature profiles | Little Ice Age | Dolostone | Annual | Permafrost temperatures | Temperature effects | Air temperature | Thermistors | Mathematical models | Porosity | Regularization | Drilling | Ice ages | Laboratories | Heat conductivity | Mountains | Thermodynamics | Accuracy | High temperature effects

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 4/2018, Volume 24, Issue 2, pp. 506 - 524

...-Coefﬁcient T oeplitz Sequences: The GL T Approach Carlo Garoni 1 · Stefano Serra-Capizzano 1 Received: 18 May 2016 / Revised: 21 November 2016 / Published online: 10...

Generalized convolution | 15B05 | Mathematics | Variable-coefficient Toeplitz matrix | 15A18 | Abstract Harmonic Analysis | Mathematical Methods in Physics | Generalized locally Toeplitz sequence | Fourier Analysis | 47B06 | Signal,Image and Speech Processing | Singular value distribution | Eigenvalue distribution | 47B35 | Approximations and Expansions | Approximating class of sequences | 15A60 | Partial Differential Equations | MATHEMATICS, APPLIED | BEHAVIOR | ASYMPTOTIC ZERO DISTRIBUTION | VARYING RECURRENCE COEFFICIENTS | MATRICES | ORTHOGONAL POLYNOMIALS | OPERATORS | Algebra

Generalized convolution | 15B05 | Mathematics | Variable-coefficient Toeplitz matrix | 15A18 | Abstract Harmonic Analysis | Mathematical Methods in Physics | Generalized locally Toeplitz sequence | Fourier Analysis | 47B06 | Signal,Image and Speech Processing | Singular value distribution | Eigenvalue distribution | 47B35 | Approximations and Expansions | Approximating class of sequences | 15A60 | Partial Differential Equations | MATHEMATICS, APPLIED | BEHAVIOR | ASYMPTOTIC ZERO DISTRIBUTION | VARYING RECURRENCE COEFFICIENTS | MATRICES | ORTHOGONAL POLYNOMIALS | OPERATORS | Algebra

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2017, Volume 86, Issue 305, pp. 1343 - 1373

A linear full elliptic second-order Partial Differential Equation (PDE), defined on a d-dimensional domain \Omega , is approximated by the isogeometric...

Isogeometric analysis | Galerkin method | Spectral distribution | Symbol | B-splines | symbol | MATHEMATICS, APPLIED | COLLOCATION LINEAR-SYSTEMS | ROBUST | STIFFNESS MATRICES | LOCALLY TOEPLITZ SEQUENCES | MULTI-ITERATIVE TECHNIQUES | isogeometric analysis

Isogeometric analysis | Galerkin method | Spectral distribution | Symbol | B-splines | symbol | MATHEMATICS, APPLIED | COLLOCATION LINEAR-SYSTEMS | ROBUST | STIFFNESS MATRICES | LOCALLY TOEPLITZ SEQUENCES | MULTI-ITERATIVE TECHNIQUES | isogeometric analysis

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2019, Volume 344, pp. 970 - 997

Alfvén-like operators are of interest in magnetohydrodynamics, which is used in plasma physics to study the macroscopic behavior of plasma. Motivated by this...

Isogeometric analysis | Alfvén-like operator | Multigrid techniques | GLT theory | Krylov preconditioning | Spectral symbol | Alfven-like operator | MULTIGRID METHODS | LOCALLY TOEPLITZ SEQUENCES | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ROBUST | MATRICES | THEOREMS | Linear systems | Magnetohydrodynamics | Plasma physics | Parameters | Computational fluid dynamics | Splines | Numerical methods | Ill-conditioning (mathematics) | Spectra | Plasma (physics) | Tensors | Dependence | Solvers | Conditioning | Iterative methods | Two dimensional analysis | Mathematics - Numerical Analysis

Isogeometric analysis | Alfvén-like operator | Multigrid techniques | GLT theory | Krylov preconditioning | Spectral symbol | Alfven-like operator | MULTIGRID METHODS | LOCALLY TOEPLITZ SEQUENCES | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ROBUST | MATRICES | THEOREMS | Linear systems | Magnetohydrodynamics | Plasma physics | Parameters | Computational fluid dynamics | Splines | Numerical methods | Ill-conditioning (mathematics) | Spectra | Plasma (physics) | Tensors | Dependence | Solvers | Conditioning | Iterative methods | Two dimensional analysis | Mathematics - Numerical Analysis

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2016, Volume 85, Issue 3, pp. 1639 - 1680

We consider a linear full elliptic second order partial differential equation in a d-dimensional domain, d >= 1, approximated by isogeometric collocation...

Isogeometric analysis | Spectral distribution | Collocation method | Symbol | B-splines | collocation method | LINEAR-SYSTEMS | symbol | MATHEMATICS, APPLIED | ROBUST | CONVERGENCE | LOCALLY TOEPLITZ SEQUENCES | MULTI-ITERATIVE TECHNIQUES | isogeometric analysis

Isogeometric analysis | Spectral distribution | Collocation method | Symbol | B-splines | collocation method | LINEAR-SYSTEMS | symbol | MATHEMATICS, APPLIED | ROBUST | CONVERGENCE | LOCALLY TOEPLITZ SEQUENCES | MULTI-ITERATIVE TECHNIQUES | isogeometric analysis

Journal Article

PAMM, ISSN 1617-7061, 10/2015, Volume 15, Issue 1, pp. 581 - 582

..., Alessandro Buccini, Marco Donatelli and Stefano Serra‐Capizzano. Iterated fractional Tikhonov regularization. Inverse Problems 31 (5) (2015)....

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 2/2018, Volume 74, Issue 2, pp. 1034 - 1059

... Feynman–Kac Equation Minghua Chen 1 · Weihua Deng 1 · Stefano Serra-Capizzano 2,3 Received: 21 November 2016 / Revised: 6 May 2017 / Accepted: 6 June 2017 / Published...

Computational Mathematics and Numerical Analysis | Algorithms | Block tridiagonal matrix | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Fractional Feynman–Kac equation | Mathematics | V-cycle multigrid method | SPACE | SCHEME | MATHEMATICS, APPLIED | DIFFUSION-EQUATIONS | TOEPLITZ MATRICES | SYSTEMS | OPERATORS | Fractional Feynman-Kac equation | Algebra | Differential equations

Computational Mathematics and Numerical Analysis | Algorithms | Block tridiagonal matrix | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Fractional Feynman–Kac equation | Mathematics | V-cycle multigrid method | SPACE | SCHEME | MATHEMATICS, APPLIED | DIFFUSION-EQUATIONS | TOEPLITZ MATRICES | SYSTEMS | OPERATORS | Fractional Feynman-Kac equation | Algebra | Differential equations

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2016, Volume 309, pp. 74 - 105

We consider large linear systems of algebraic equations arising from the Finite Element approximation of coupled partial differential equations. As case study...

Coupled systems of PDEs | GLT sequence | Schur complement | Toeplitz matrix | Joint eigenvalue distribution | DEFORMATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ROBUST | MATRICES | CONVERGENCE | SYSTEMS | MULTI-ITERATIVE TECHNIQUES | Case studies | Analysis | Algebra | Mayas | Differential equations

Coupled systems of PDEs | GLT sequence | Schur complement | Toeplitz matrix | Joint eigenvalue distribution | DEFORMATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ROBUST | MATRICES | CONVERGENCE | SYSTEMS | MULTI-ITERATIVE TECHNIQUES | Case studies | Analysis | Algebra | Mayas | Differential equations

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2006, Volume 419, Issue 1, pp. 180 - 233

Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of...

Toeplitz (and Generalized Locally Toeplitz) sequence | Algebra of sequences | Fourier Analysis | Generating function | Sparsely vanishing sequence or function | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | OPTIMAL CONVERGENCE | OPERATIONS | generating function | Fourier analysis | EIGENVALUES | algebra of sequences | BLOCK TOEPLITZ MATRICES | COEFFICIENTS | SINGULAR-VALUES | ITERATIVE METHODS | sparsely vanishing sequence or function | SPECTRA | OPERATORS

Toeplitz (and Generalized Locally Toeplitz) sequence | Algebra of sequences | Fourier Analysis | Generating function | Sparsely vanishing sequence or function | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | OPTIMAL CONVERGENCE | OPERATIONS | generating function | Fourier analysis | EIGENVALUES | algebra of sequences | BLOCK TOEPLITZ MATRICES | COEFFICIENTS | SINGULAR-VALUES | ITERATIVE METHODS | sparsely vanishing sequence or function | SPECTRA | OPERATORS

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2015, Volume 284, pp. 230 - 264

We consider fast solvers for large linear systems arising from the Galerkin approximation based on B-splines of classical d-dimensional elliptic problems, d≥1,...

Isogeometric analysis | [formula omitted]-splines | Galerkin method | PCG, multigrid, and multi-iterative methods | Toeplitz matrices | Symbol | B-splines | SEQUENCES | multigrid | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PCG | multi-iterative methods | EIGENVECTORS | SPECTRUM | FOURIER-ANALYSIS | Linear systems | Immunoglobulin A | Analysis | Methods | Design engineering | Approximation | Mathematical analysis | Symbols | Mathematical models | Galerkin methods | Optimization | Convergence

Isogeometric analysis | [formula omitted]-splines | Galerkin method | PCG, multigrid, and multi-iterative methods | Toeplitz matrices | Symbol | B-splines | SEQUENCES | multigrid | PRECONDITIONERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PCG | multi-iterative methods | EIGENVECTORS | SPECTRUM | FOURIER-ANALYSIS | Linear systems | Immunoglobulin A | Analysis | Methods | Design engineering | Approximation | Mathematical analysis | Symbols | Mathematical models | Galerkin methods | Optimization | Convergence

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2017, Volume 55, Issue 1, pp. 31 - 62

We consider the stiffness matrices arising from the Galerkin B-spline isogeometric analysis discretization of classical elliptic problems. By exploiting their...

Isogeometric analysis | Multigrid methods | Toeplitz matrices | Preconditioning | B-splines | multigrid methods | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | OPTIMAL CONVERGENCE | FINITE-ELEMENTS | SEQUENCES | preconditioning | PRECONDITIONERS | STIFFNESS MATRICES | SPECTRAL-ANALYSIS | ITERATIVE TECHNIQUES | FOURIER-ANALYSIS | isogeometric analysis

Isogeometric analysis | Multigrid methods | Toeplitz matrices | Preconditioning | B-splines | multigrid methods | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | OPTIMAL CONVERGENCE | FINITE-ELEMENTS | SEQUENCES | preconditioning | PRECONDITIONERS | STIFFNESS MATRICES | SPECTRAL-ANALYSIS | ITERATIVE TECHNIQUES | FOURIER-ANALYSIS | isogeometric analysis

Journal Article

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Exact formulae and matrix-less eigensolvers for block banded symmetric Toeplitz matrices

BIT. Numerical mathematics, ISSN 1572-9125, 2018, Volume 58, Issue 4, pp. 937 - 968

... Toeplitz matrices Sven-Erik Ekström 1 · Isabella Furci 2 · Stefano Serra-Capizzano 1,2 Received: 9 March 2018 / Accepted: 21 June 2018 / Published online: 3 July 2018...

MSC 65B05 | Computational Mathematics and Numerical Analysis | MSC 65D05 | Numeric Computing | Mathematics | Asymptotic eigenvalue expansion | MSC 65F15 | Extrapolation | Polynomial interpolation | Eigenvalues | Mathematics, general | Block matrices | MSC 15B05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Algorithms

MSC 65B05 | Computational Mathematics and Numerical Analysis | MSC 65D05 | Numeric Computing | Mathematics | Asymptotic eigenvalue expansion | MSC 65F15 | Extrapolation | Polynomial interpolation | Eigenvalues | Mathematics, general | Block matrices | MSC 15B05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Algorithms

Journal Article

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, ISSN 1537-9582, 05/2019, Volume 35, pp. 204 - 222

The theory of block generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the spectral distribution of block-structured matrices...

MATHEMATICS | Block generalized locally Toeplitz sequences | Matrix functions | APPROXIMATIONS | Differential eigenvalue problems | SINGULAR-VALUES | ISOGEOMETRIC ANALYSIS | Higher-order isogeometric Galerkin method | B-splines

MATHEMATICS | Block generalized locally Toeplitz sequences | Matrix functions | APPROXIMATIONS | Differential eigenvalue problems | SINGULAR-VALUES | ISOGEOMETRIC ANALYSIS | Higher-order isogeometric Galerkin method | B-splines

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2007, Volume 45, Issue 2, pp. 746 - 769

...SIAM J. NUMER. ANAL. c Vol. 45, No. 2, pp. 746769 ON THE ASYMPTOTIC SPECTRUM OF FINITE ELEMENT MATRIX SEQUENCES BERNHARD BECKERMANN AND STEFANO SERRA-CAPIZZANO...

Stiffness matrix | Triangulation | Mathematical sequences | Approximation | Spectral theory | Eigenvalues | Matrices | Stiffness | Stencils | Vertices | Asymptotic eigenvalue distribution | Finite element methods | Matrix sequence | asymptotic eigenvalue distribution | MATHEMATICS, APPLIED | finite element methods | THEOREMS | DISCRETE POISSON EQUATION | matrix sequence | CONVERGENCE | TOEPLITZ SEQUENCES | COLLOCATION

Stiffness matrix | Triangulation | Mathematical sequences | Approximation | Spectral theory | Eigenvalues | Matrices | Stiffness | Stencils | Vertices | Asymptotic eigenvalue distribution | Finite element methods | Matrix sequence | asymptotic eigenvalue distribution | MATHEMATICS, APPLIED | finite element methods | THEOREMS | DISCRETE POISSON EQUATION | matrix sequence | CONVERGENCE | TOEPLITZ SEQUENCES | COLLOCATION

Journal Article

Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2015, Volume 284, pp. 1120 - 1146

We consider fast solvers for the large linear systems coming from the Isogeometric Analysis (IgA) collocation approximation based on B-splines of full elliptic...

Isogeometric analysis | Collocation method | Toeplitz matrices | P-GMRES, multigrid, and multi-iterative methods | Symbol | B-splines | Multi-iterative methods | P-GMRES | Multigrid | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | Linear systems | Immunoglobulin A | Analysis | Methods | Collocation | Partial differential equations | Mathematical analysis | Symbols | Solvers | Mathematical models | Spectra | Optimization

Isogeometric analysis | Collocation method | Toeplitz matrices | P-GMRES, multigrid, and multi-iterative methods | Symbol | B-splines | Multi-iterative methods | P-GMRES | Multigrid | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | Linear systems | Immunoglobulin A | Analysis | Methods | Collocation | Partial differential equations | Mathematical analysis | Symbols | Solvers | Mathematical models | Spectra | Optimization

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2019, Volume 579, pp. 32 - 50

The singular value and spectral distribution of Toeplitz matrix sequences with Lebesgue integrable generating functions is well studied. Early results were...

Toeplitz matrices | Circulant preconditioners | Hankel matrices | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | SINGULAR-VALUES

Toeplitz matrices | Circulant preconditioners | Hankel matrices | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | SINGULAR-VALUES

Journal Article

Calcolo, ISSN 0008-0624, 2014, Volume 51, Issue 4, pp. 639 - 659

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) A matrix ... of size ... is called ...-circulant if ..., while a matrix ... is...

Multigrid methods | Circulants | Toeplitz | G-Circulants | Spectral distributions | Hankel | g-Toeplitz

Multigrid methods | Circulants | Toeplitz | G-Circulants | Spectral distributions | Hankel | g-Toeplitz

Journal Article

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Multigrid methods for cubic spline solution of two point (and 2D) boundary value problems

Applied Numerical Mathematics, ISSN 0168-9274, 06/2016, Volume 104, pp. 15 - 29

In this paper we propose a scheme based on cubic splines for the solution of the second order two point boundary value problems. The solution of the algebraic...

Finite elements | Multigrid methods | Toeplitz matrices | Symbol | Spectral analysis | Cubic splines (Csplines) | MATHEMATICS, APPLIED | EQUATIONS | Boundary value problems | Splines | Mathematical analysis | Eigenvalues | Mathematical models | Two dimensional | Optimization | equations | Mathematics | Matematik

Finite elements | Multigrid methods | Toeplitz matrices | Symbol | Spectral analysis | Cubic splines (Csplines) | MATHEMATICS, APPLIED | EQUATIONS | Boundary value problems | Splines | Mathematical analysis | Eigenvalues | Mathematical models | Two dimensional | Optimization | equations | Mathematics | Matematik

Journal Article

Numerical Algorithms, ISSN 1017-1398, 7/2018, Volume 78, Issue 3, pp. 867 - 893

Bogoya, Böttcher, Grudsky, and Maximenko have recently obtained the precise asymptotic expansion for the eigenvalues of a sequence of Toeplitz matrices {T n...

Mass and stiffness matrix | Eigenvalue asymptotics | Numeric Computing | 15B05 | Theory of Computation | Extrapolation | Algorithms | Algebra | Numerical Analysis | Polynomial interpolation | Computer Science | Eigenvalues | 65D05 | (Preconditioned) Toeplitz matrix | 65F15 | 65B05 | SIMPLE-LOOP SYMBOLS | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | STRATEGIES

Mass and stiffness matrix | Eigenvalue asymptotics | Numeric Computing | 15B05 | Theory of Computation | Extrapolation | Algorithms | Algebra | Numerical Analysis | Polynomial interpolation | Computer Science | Eigenvalues | 65D05 | (Preconditioned) Toeplitz matrix | 65F15 | 65B05 | SIMPLE-LOOP SYMBOLS | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | STRATEGIES

Journal Article

20.