Search
Search Results
-
Hilbert Spaces
Inner products are generalizations of the dot product in $$\mathbb...
-
Identification of a Time Dependent Source Function in a Parabolic Inverse Problem Via Finite Element Approach
In the present paper, we study one-dimensional inverse source problem of identifying a time-dependent source function from the over-specification...
-
Stochastic Calculus with n-Covariations
This chapter develops the calculus via regularizations for non-finite quadratic variation processes that have a finite n-variation for n > 2. If...
-
Perseus: a simple and optimal high-order method for variational inequalities
This paper settles an open and challenging question pertaining to the design of simple and optimal high-order methods for solving smooth and monotone...
-
Numerical solutions of inverse time fractional coupled Burgers’ equations by the Chebyshev wavelet method
In this paper, we investigate an inverse problem of recovering the unknown boundary conditions in the time fractional coupled Burgers’ equations...
-
Zeroth-Order Nonconvex Stochastic Optimization: Handling Constraints, High Dimensionality, and Saddle Points
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on...
-
Optimization: Regression
The problem central to this chapter, and the one that follows, is easy to state: given a function...
-
Spectral Stability of Shock-fronted Travelling Waves Under Viscous Relaxation
Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Li et al. (Physica D...
-
A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation
The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy...
-
Spectrally-Consistent Regularization of Navier–Stokes Equations
The incompressible Navier–Stokes equations form an excellent mathematical model for turbulent flows. However, direct simulations at high Reynolds...
-
A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex...
-
Smooth projection of mortality improvement rates: a Bayesian two-dimensional spline approach
This paper proposes a spline mortality model for generating smooth projections of mortality improvement rates. In particular, we follow the...
-
Estimating the Size of an Open Population with Massive Datasets Based on a Generalized Varying-Coefficient Model
A generalized varying-coefficient model is proposed to estimate a population size at a specific time from multiple lists of an open population. The...
-
An inverse problem for investigating the time-dependent coefficient in a higher-order equation
In this paper, we considered an inverse problem of recovering the time-dependent potential coefficient, for the first time, in the sixth-order...
-
Group LASSO for Change-points in Functional Time Series
Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a...
-
Nonlinear Methods
So far, we have exclusively considered model-free and linear models for regression, since (1) the theory is simple(er), (2) (imputation) models are...
-
On the use of third-order models with fourth-order regularization for unconstrained optimization
In a recent paper (Birgin et al. in Math Program 163(1):359–368,
2017 ), it was shown that, for the smooth unconstrained optimization problem,...
-
AAA interpolation of equispaced data
We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced samples. Although it is always...
-
New computational methods for inverse wave scattering with a new filtering technique
This note is concerned with inverse wave scattering in one and two dimensional domains. It seeks to recover an unknown function based on measurements...
-
SI Epidemic Model Applied to COVID-19 Data in Mainland China
Estimating the average transmission rate is one of the most crucial challenges in the epidemiology of communicable diseases. This rate conditions the...