Faster Arbitrary-Precision Dot Product and Matrix Multiplication

Johansson, Fredrik

doi:10.1109/arith.2019.00012

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…48 Simulations of the impedance of the full cell/electrode/individual circuit elements, and complex nonlinear least squares fitting of the equivalent circuit models to the data was performed using software programmed in Python 49 which relies on the scientific Python stack, [50][51][52] and for the 1D/2D elements the library mpmath was used to provide higher precision complex floating-point arithmetic. 53 Tortuosity estimation from TLMs.-The ionic resistivity in the infiltrated pore with length L, R ion,L [ cm] calculated from the TLMs is correlated to the effective electrode pore tortuosity τ el through the equation:…”

Section: Methodsmentioning

confidence: 99%

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell

Scipioni¹,

Jørgensen²,

Graves³

et al. 2017

J. Electrochem. Soc.

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In this work an Equivalent Circuit Model (ECM) is developed and used to model impedance spectra measured on a commercial 26650 LiFePO 4 /Graphite cylindrical cell. The ECM is based on measurements and modeling of impedance spectra recorded separately on cathode (LiFePO 4 ) and anode (Graphite) samples, harvested from the commercial cell. Modeling of the single-electrode impedance spectra provided information about the electronic and ionic resistance in the porous composite electrodes, as well as the solid state diffusion. Focused Ion Beam (FIB)/Scanning Electron Microscopy (SEM) of anode and cathode samples was used to make 3-D maps of the electrode microstructures and to obtain microstructural data for the ECM. The cylindrical cell continues to be one of the most widely used packaging styles for primary and secondary batteries. The advantages are ease of manufacture and good mechanical stability. The tubular cylinder can withstand high internal pressures without deforming.

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Section: Methodsmentioning

confidence: 99%

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell

Scipioni¹,

Jørgensen²,

Graves³

et al. 2017

J. Electrochem. Soc.

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“…Exact convolutions divide a convolution operation into subproblems that involve the multiplication of the input vector with constants [13]. To optimize multiplication, related work [14]- [17] uses an adder graph tree structure that expresses addition, subtraction, and bit shifting.…”

Section: Related Workmentioning

confidence: 99%

Efficient, Geometry-Based Convolution

2022

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Several computationally intensive applications in machine learning, signal processing, and computer vision call for convolution between a fixed vector and each of the incoming vectors. Often, the convolution need not be exact because a subsequent processing unit, such as an activation function in a neuron network or a visual unit in image processing, can tolerate a computational error, hence allowing the optimization of the convolution algorithm. This paper develops a method of approximate convolution and quantifies its performance in software and hardware. The key idea is to take advantage of the known fixed vector, view a convolution as a dot product, and approximate the angles between the fixed vector and an incoming vector geometrically. We evaluate the proposed method in terms of the accuracy, running time complexity, and hardware power consumption on the field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) hardware platforms. In a benchmark test, the accuracy of the approximate convolution is 3.7% lower than that of the exact convolution, a tolerable loss for machine learning and signal processing. The proposed method reduces the number of operations in the hardware and reduces the power consumption of conventional convolution and the existing approximate convolution by approximately 20% and 10%, respectively, while maintaining the same throughput and latency. We also test the proposed method on 2D convolution and convolutional neural network (CNN). The proposed method reduces the complexity, power consumption for 2D convolution, power consumption for CNN of the conventional method by approximately 22%, 25%, and 13%, respectively. The proposed method of approximate convolution trades off accuracy with running time complexity and hardware power consumption, and it has practical utility in computationally intensive tasks that tolerate a margin of convolutional error.INDEX TERMS Convolution, dot product, power consumption, field programmable gate array (FPGA)

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“…• Berk (Berkowitz), Alg1 and Alg2 as in the previous section. All algorithms were implemented in Arb [18] which uses the accelerated dot product and matrix multiplication algorithms described in [19]. The LU, LU2, Alg1 and Alg2 implementations benefit from fast matrix multiplication while Hess, Hess2, Eig and Berk do not.…”

Section: 21mentioning

confidence: 99%

On a fast and nearly division-free algorithm for the characteristic polynomial

Johansson¹

2020

Preprint

Self Cite

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We review the Preparata-Sarwate algorithm, a simple O(n 3.5 ) method for computing the characteristic polynomial, determinant and adjugate of an n×n matrix using only ring operations together with exact divisions by small integers. The algorithm is a baby-step giant-step version of the more well-known Faddeev-Leverrier algorithm. We make a few comments about the algorithm and evaluate its performance empirically.

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Faster Arbitrary-Precision Dot Product and Matrix Multiplication

Cited by 9 publications

References 17 publications

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell

Efficient, Geometry-Based Convolution

On a fast and nearly division-free algorithm for the characteristic polynomial

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Faster Arbitrary-Precision Dot Product and Matrix Multiplication

Cited by 9 publications

References 17 publications

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO4/Graphite 26650 Cylindrical Cell

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO4/Graphite 26650 Cylindrical Cell

Efficient, Geometry-Based Convolution

On a fast and nearly division-free algorithm for the characteristic polynomial

Contact Info

Product

Resources

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A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell

A Physically-Based Equivalent Circuit Model for the Impedance of a LiFePO₄/Graphite 26650 Cylindrical Cell