Bertaccini et al., 2019 - Google Patents
Efficient approximation of functions of some large matrices by partial fraction expansionsBertaccini et al., 2019
View PDF- Document ID
- 12692938844664212369
- Author
- Bertaccini D
- Popolizio M
- Durastante F
- Publication year
- Publication venue
- International Journal of Computer Mathematics
External Links
Snippet
Some important applicative problems require the evaluation of functions Ψ of large and sparse and/or localized matrices A. Popular and interesting techniques for computing Ψ (A) and Ψ (A) v, where v is a vector, are based on partial fraction expansions. However, some of …
- 239000011159 matrix material 0 abstract description 97
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/50—Computer-aided design
- G06F17/5009—Computer-aided design using simulation
- G06F17/5036—Computer-aided design using simulation for analog modelling, e.g. for circuits, spice programme, direct methods, relaxation methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/50—Computer-aided design
- G06F17/5009—Computer-aided design using simulation
- G06F17/5018—Computer-aided design using simulation using finite difference methods or finite element methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/50—Computer-aided design
- G06F17/5009—Computer-aided design using simulation
- G06F17/504—Formal methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
- G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
- G06F7/724—Finite field arithmetic
- G06F7/726—Inversion; Reciprocal calculation; Division of elements of a finite field
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/30—Information retrieval; Database structures therefor; File system structures therefor
- G06F17/30286—Information retrieval; Database structures therefor; File system structures therefor in structured data stores
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F11/00—Error detection; Error correction; Monitoring
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F19/00—Digital computing or data processing equipment or methods, specially adapted for specific applications
- G06F19/70—Chemoinformatics, i.e. data processing methods or systems for the retrieval, analysis, visualisation, or storage of physicochemical or structural data of chemical compounds
- G06F19/708—Chemoinformatics, i.e. data processing methods or systems for the retrieval, analysis, visualisation, or storage of physicochemical or structural data of chemical compounds for data visualisation, e.g. molecular structure representations, graphics generation, display of maps or networks or other visual representations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F2207/00—Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F1/00—Details of data-processing equipment not covered by groups G06F3/00 - G06F13/00, e.g. cooling, packaging or power supply specially adapted for computer application
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F19/00—Digital computing or data processing equipment or methods, specially adapted for specific applications
- G06F19/10—Bioinformatics, i.e. methods or systems for genetic or protein-related data processing in computational molecular biology
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING; COUNTING
- G06F—ELECTRICAL DIGITAL DATA PROCESSING
- G06F2217/00—Indexing scheme relating to computer aided design [CAD]
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Margossian | A review of automatic differentiation and its efficient implementation | |
Dai et al. | An explicit method for simulating non-Gaussian and non-stationary stochastic processes by Karhunen-Loève and polynomial chaos expansion | |
Kim et al. | Modeling strongly non-Gaussian non-stationary stochastic processes using the iterative translation approximation method and Karhunen–Loève expansion | |
Minchev et al. | A review of exponential integrators for first order semi-linear problems | |
Diethelm et al. | Pitfalls in fast numerical solvers for fractional differential equations | |
Huang et al. | Accelerating the convergence of spectral deferred correction methods | |
Dehghan | Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement | |
Di Renzo et al. | Numerical stochastic perturbation theory for full QCD | |
Minden et al. | Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations | |
Johns et al. | A two-stage ensemble Kalman filter for smooth data assimilation | |
Field Jr et al. | On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems | |
Hu et al. | A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations | |
Aceto et al. | Rational Krylov methods for functions of matrices with applications to fractional partial differential equations | |
Zlotnick et al. | FINITE ELEMENT METHOD WITH DISCRETE TRANSPARENT BOUNDARY CONDITIONS FOR THE TIME-DEPENDENT 1D SCHRÖDINGER EQUATION. | |
Itkin | Efficient solution of backward jump-diffusion partial integro-differential equations with splitting and matrix exponentials | |
Garmatter et al. | A reduced basis Landweber method for nonlinear inverse problems | |
Chib | Markov chain monte carlo technology | |
Garrappa | A family of Adams exponential integrators for fractional linear systems | |
Alzahrani et al. | Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction–diffusion equations | |
Kiser et al. | Classical and quantum cost of measurement strategies for quantum-enhanced auxiliary field quantum monte carlo | |
Bertaccini et al. | Efficient approximation of functions of some large matrices by partial fraction expansions | |
Mu | A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes | |
Tan et al. | Temporal second-order fully discrete two-grid methods for nonlinear time-fractional variable coefficient diffusion-wave equations | |
Cao et al. | Structure-preserving numerical schemes for Lindblad equations | |
Xu et al. | Efficient algorithms for computing multidimensional integral fractional Laplacians via spherical means |