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Time-Limited Balanced Truncation for Data Assimilation Problems
Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection...
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Balanced Truncation Model Reduction for 3D Linear Magneto-Quasistatic Field Problems
We consider linear magneto-quasistatic field equations which arise in simulation of low-frequency electromagnetic devices coupled to electrical...
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Balanced truncation of linear time-invariant systems over finite-frequency ranges
This paper discusses model order reduction of linear time-invariant (LTI) systems over limited frequency intervals within the framework of balanced...
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Efficient techniques for numerical solutions of Fisher’s equation using B-spline finite element methods
This study presents a numerical solution of Fisher’s equation. For time integration, Crank–Nicolson and fourth-order one-step implicit schemes are...
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Restart, deflation and truncation
In this chapter we describe techniques that have been used to control the storage and the complexity in methods like GMRES and FOM which use long...
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A Reduced-Basis Polynomial-Chaos Approach with a Multi-parametric Truncation Scheme for Problems with Uncertainties
Polynomial-chaos (PC) expansions constitute an invaluable tool for the investigation of uncertainty quantification problems, yet minimizing the...
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Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct...
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Implicit Integration of Nonlinear Evolution Equations on Tensor Manifolds
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial...
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Algebraic topological techniques for elliptic problems involving fractional Laplacian
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus...
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Multiple Solutions for a Kirchhoff-type Problem with Vanishing Nonlocal Term and Fractional p-Laplacian
The goal of the paper is to investigate a Kirchhoff-type elliptic problem driven by a generalized nonlocal fractional p -Laplacian whose nonlocal term...
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Maximum Full Likelihood Approach to Randomly Truncated Data
Truncated data are commonly observed in economics, epidemiology, and other fields. The analysis of truncated data is challenging because the observed...
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From low-rank retractions to dynamical low-rank approximation and back
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates...
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On the number of terms in the COS method for European option pricing
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to...
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Soliton Solutions for Coupled Nonlinear Generalized Zakharov Equations with Anti-cubic Nonlinearity Using Various Techniques
This study introduces novel exact solutions for the coupled nonlinear generalized Zakharov equations with anti-cubic nonlinearity. Utilizing a...
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Multiple Nontrivial Solutions for Superlinear Double Phase Problems Via Morse Theory
The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the...
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Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems
The solution of minimum-time feedback optimal control problems is generally achieved using the dynamic programming approach, in which the value...
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Multivariate form of Hermite sampling series
In this paper, we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial...
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Adaptive Integration of Nonlinear Evolution Equations on Tensor Manifolds
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call...
