Generalized Tractability for Multivariate Problems Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability

2009 ◽  
Vol 9 (4) ◽  
pp. 431-460 ◽  
Author(s):  
Michael Gnewuch ◽  
Henryk Woźniakowski
Keyword(s):  
Tensor Product ◽  
Multivariate Problems ◽  
Linear Information

scholarly journals Weighted Tensor Product Algorithms for Linear Multivariate Problems

1999 ◽  
Vol 15 (3) ◽  
pp. 402-447 ◽  
Author(s):  
G.W Wasilkowski ◽  
H Woźniakowski
Keyword(s):  
Tensor Product ◽  
Multivariate Problems

scholarly journals On the Power of Standard Information for Tractability for L2- Approximation in the Randomized Setting

2022 ◽  
pp. 1-29
Author(s):  
Wanting Lu ◽  
Heping Wang
Keyword(s):  
Separable Hilbert Space ◽  
Absolute Error ◽  
Multivariate Functions ◽  
Error Criterion ◽  
Open Problems ◽  
Normalized Error ◽  
L2 Norm ◽  
Multivariate Problems ◽  
Linear Information ◽  
Standard Information

We study the approximation of multivariate functions from a separable Hilbert space in the randomized setting with the error measured in the weighted L2 norm. We consider algorithms that use standard information Λstd consisting of function values or general linear information Λall consisting of arbitrary linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability in the randomized setting for Λstd and Λall for the normalized or absolute error criterion. For the normalized error criterion, we show that the power of Λstd is the same as that of Λall for all notions of exponential tractability and some notions of algebraic tractability without any condition. For the absolute error criterion, we show that the power of Λstd is the same as that of Λall for all notions of algebraic and exponential tractability without any condition. Specifically, we solve Open Problems 98, 101, 102 and almost solve Open Problem 100 as posed by E.Novak and H.Wo´zniakowski in the book: Tractability of Multivariate Problems, Volume III: Standard Information for Operators, EMS Tracts in Mathematics, Zürich, 2012.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal

On degeneracy problem of NFSRs via semi-tensor product

2020 ◽  
Author(s):  
Xinyu Zhao ◽  
Biao Wang ◽  
Shuqian Zhu ◽  
Jun-e Feng
Keyword(s):  
Tensor Product ◽  
Degeneracy Problem

Implementing Residual Income Valuation With Linear Information Dynamics

1999 ◽  
Vol 74 (1) ◽  
pp. 1-28 ◽  
Author(s):  
James N. Myers
Keyword(s):  
Time Series ◽  
Firm Value ◽  
Residual Income ◽  
Accounting System ◽  
Information Dynamics ◽  
No Arbitrage ◽  
Book Value ◽  
Residual Income Valuation ◽  
Accounting Numbers ◽  
Linear Information

Residual income (RI) valuation is a method of estimating firm value based on expected future accounting numbers. This study documents the necessity of using linear information models (LIMs) of the time series of accounting numbers in valuation. I find that recent studies that make ad hoc modifications to the LIMs contain internal inconsistencies and violate the no arbitrage assumption. I outline a method for modifying the LIMs while preserving internal consistency. I also find that when estimated as a time series, the LIMs of Ohlson (1995), and Feltham and Ohlson (1995) provide value estimates no better than book value alone. By comparing the implied price coefficients to coefficients from a price level regression, I find that the models imply inefficient weightings on the accounting numbers. Furthermore, the median conservatism parameter of Feltham and Ohlson (1995) is significantly negative, contrary to the model's prediction, for even the most conservative firms. To explain these failures, I estimate a LIM from a more carefully modeled accounting system that provides two parameters of conservatism (the income parameter and the book value parameter). However, this model also fails to capture the true stochastic relationship among accounting variables. More complex models tend to provide noisier estimates of firm value than more parsimonious models.

On the Buchstaber Subring in MSp∗

1998 ◽  
Vol 5 (5) ◽  
pp. 401-414
Author(s):  
M. Bakuradze
Keyword(s):  
Tensor Product ◽  
Characteristic Classes ◽  
Generalized Quaternion ◽  
Symplectic Cobordisms

Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

scholarly journals Fractal Frames of Functions on the Rectangle

2021 ◽  
Vol 5 (2) ◽  
pp. 42
Author(s):  
María A. Navascués ◽  
Ram Mohapatra ◽  
Md. Nasim Akhtar
Keyword(s):  
Tensor Product ◽  
Product Space ◽  
Integrable Function ◽  
Two Dimensional ◽  
Tensor Product Space ◽  
Fractal Functions

In this paper, we define fractal bases and fractal frames of L2(I×J), where I and J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of L2(I×J) with the tensor product space L2(I)⨂L2(J). First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of L2(I×J) composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.

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