Ismail Nikoufar A PERSPECTIVE APPROACH FOR
... will discuss on α, β, where we give a complete characterization of some well known theorems including Lieb and Ando theorems. The following theorem is a more generalized version of [NEE, Theorem 1.1]. Theorem 4. Assume that λ, γ are real numbers. (i) The operator pλ, γq-geometric mean is jointly con ...
... will discuss on α, β, where we give a complete characterization of some well known theorems including Lieb and Ando theorems. The following theorem is a more generalized version of [NEE, Theorem 1.1]. Theorem 4. Assume that λ, γ are real numbers. (i) The operator pλ, γq-geometric mean is jointly con ...
Non-standard Norms and Robust Estimates for Saddle Point Problems
... It is well-known that IH is an isometric isomorphism between H and its dual space ...
... It is well-known that IH is an isometric isomorphism between H and its dual space ...
Computing the square roots of matrices with central symmetry 1
... Theory and algorithms for structured matrices have been a topic of research for many years. There are many applications that generate structured matrices and by exploiting the structure one may be able to design faster and/or more accurate algorithms; furthermore, structure may also help in producin ...
... Theory and algorithms for structured matrices have been a topic of research for many years. There are many applications that generate structured matrices and by exploiting the structure one may be able to design faster and/or more accurate algorithms; furthermore, structure may also help in producin ...
Module 3: 3D Constitutive Equations Lecture 12: Constitutive
... In this section, based on the work done by Lempriere we are going to assess the implications of this thermodynamic requirement (positive definiteness of strain energy) for orthotropic materials. The sum of work done by all stress components must be positive, otherwise energy will be created. This ...
... In this section, based on the work done by Lempriere we are going to assess the implications of this thermodynamic requirement (positive definiteness of strain energy) for orthotropic materials. The sum of work done by all stress components must be positive, otherwise energy will be created. This ...
MA75 - Sparse over-determined system: weighted least squares
... The INTEGER array ICNTL contains integer control values. It is initialized to default values by MA75I/ID and may subsequently be reset by the user. ICNTL(1) (was LP) is used by the subroutines as the output stream for error messages. If it is set to zero these messages will be suppressed. The defaul ...
... The INTEGER array ICNTL contains integer control values. It is initialized to default values by MA75I/ID and may subsequently be reset by the user. ICNTL(1) (was LP) is used by the subroutines as the output stream for error messages. If it is set to zero these messages will be suppressed. The defaul ...
Rotation Matrices 2
... capture techniques. These marker locations are used to estimate orthogonal unit vectors iprox,jprox,kprox for the proximal segment and idistal,jdistal,kdistal for the distal segment, at each time point. Since the markers are in the GRS, the unit vectors are also expressed in the GRS. We assume vecto ...
... capture techniques. These marker locations are used to estimate orthogonal unit vectors iprox,jprox,kprox for the proximal segment and idistal,jdistal,kdistal for the distal segment, at each time point. Since the markers are in the GRS, the unit vectors are also expressed in the GRS. We assume vecto ...
PARALLEL IMPLEMENTATION OF RELATIONAL ALGEBRA
... relational databases. We first propose a new associative algorithm for the multicomparand search and its implementation on the MCA-machine. It generalizes the Falkoff associative algorithm [1] that simultaneously selects those rows in a given matrix that coincide with a given pattern. Then we consid ...
... relational databases. We first propose a new associative algorithm for the multicomparand search and its implementation on the MCA-machine. It generalizes the Falkoff associative algorithm [1] that simultaneously selects those rows in a given matrix that coincide with a given pattern. Then we consid ...
I
... webpages, consumers, etc) yield a vector ai ∈ Rn where n = number of features of i; collection of m such objects, A = [a1 , . . . , am ] may be regarded as an m-by-n matrix, e.g. gene × microarray matrices in bioinformatics, terms × documents matrices in text mining, facial images × individuals matr ...
... webpages, consumers, etc) yield a vector ai ∈ Rn where n = number of features of i; collection of m such objects, A = [a1 , . . . , am ] may be regarded as an m-by-n matrix, e.g. gene × microarray matrices in bioinformatics, terms × documents matrices in text mining, facial images × individuals matr ...
Fast Polynomial Factorization Over High
... which already the Berlekamp [3] algorithm achieves (see also [21, 8], and [6]). Here we focus on the latter case when additionally q = pk with p prime and where Fq is represented in the Kronecker style as Fp [z]=('(z)), where ' is an irreducible polynomial over Fp of degree k. For the sake of introd ...
... which already the Berlekamp [3] algorithm achieves (see also [21, 8], and [6]). Here we focus on the latter case when additionally q = pk with p prime and where Fq is represented in the Kronecker style as Fp [z]=('(z)), where ' is an irreducible polynomial over Fp of degree k. For the sake of introd ...
Fast Polynomial Factorization Over High Algebraic
... algorithms stated above, the number of fixed precision integer operations for factoring a polynomial of degree n over Fq is then O(n(log q)2+o(1) ), or, in terms of a, O(n3+2a+o(1) ). In this paper we show that under the described circumstances the fixed precision complexity of computing all irreduc ...
... algorithms stated above, the number of fixed precision integer operations for factoring a polynomial of degree n over Fq is then O(n(log q)2+o(1) ), or, in terms of a, O(n3+2a+o(1) ). In this paper we show that under the described circumstances the fixed precision complexity of computing all irreduc ...
Linearly independence Definition: Consider a set of n
... {K 1 ,K 2 ,K 3 ,K 4 } span V 3 (R), and is not linearly independent. {K 1 ,K 2 ,K 3 } span V 3 (R), and is linearly independent. {K 1 ,K 2 ,K 4 } does not span V 3 (R), and is not linearly independent. {K 1 ,K 2 } does not span V 3 (R), and is linearly independent. Definition: The mi ...
... {K 1 ,K 2 ,K 3 ,K 4 } span V 3 (R), and is not linearly independent. {K 1 ,K 2 ,K 3 } span V 3 (R), and is linearly independent. {K 1 ,K 2 ,K 4 } does not span V 3 (R), and is not linearly independent. {K 1 ,K 2 } does not span V 3 (R), and is linearly independent. Definition: The mi ...
Math 215A HW3 Solution to Problem 1
... π : GLn (R) → GLn (R)+ /(GLn−1 (R)+ ×Rn−1 ) can be written as π = f ◦f . Hence this is a homeomorphism and GLn (R)+ /(GLn−1 (R)+ × Rn−1 ) is connected. By the lemmata above, since GLn (R)+ /(GLn−1 (R)+ ×Rn−1 ) and (GLn−1 (R)+ ×Rn−1 ) are connected so is GLn (R)+ . This exact same argument may be app ...
... π : GLn (R) → GLn (R)+ /(GLn−1 (R)+ ×Rn−1 ) can be written as π = f ◦f . Hence this is a homeomorphism and GLn (R)+ /(GLn−1 (R)+ × Rn−1 ) is connected. By the lemmata above, since GLn (R)+ /(GLn−1 (R)+ ×Rn−1 ) and (GLn−1 (R)+ ×Rn−1 ) are connected so is GLn (R)+ . This exact same argument may be app ...
M04/01
... However when associativity is dropped many of these tools are no longer available and often examples are constructed by indicating a multiplication table. A generalization of Ward quasigroups is obtained when the operation x ∗ y = x · y −1 is based on a loop (G, ·) with the antiautomorphic inverse p ...
... However when associativity is dropped many of these tools are no longer available and often examples are constructed by indicating a multiplication table. A generalization of Ward quasigroups is obtained when the operation x ∗ y = x · y −1 is based on a loop (G, ·) with the antiautomorphic inverse p ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.