Numer. Linear Algebra Appl.
 1997
DOI: 10.1002/(sici)1099-1506(199703/04)4:2<103::aid-nla101>3.0.co;2-j
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Stabilizing the Hierarchical Basis by Approximate Wavelets, I: Theory

Panayot S. Vassilevski
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Junping Wang
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Cited by 75 publications

(50 citation statements)
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“…Although not observed in [34,35], the result does not require substantial modification for locally refined meshes. Let e j := (Q j − Q j )u be the error; then the following holds.…”
Section: Lower Bound In the Norm Equivalence The Jackson Inequality mentioning
confidence: 78%
“…Before getting to the stability result we remark that the existing perturbation analysis of WHB is one of the primary insights in [34,35]. Although not observed in [34,35], the result does not require substantial modification for locally refined meshes.…”
Section: Lower Bound In the Norm Equivalence The Jackson Inequality mentioning
confidence: 93%
See 1 more Smart Citation
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…Although not observed in [34,35], the result does not require substantial modification for locally refined meshes. Let e j := (Q j − Q j )u be the error; then the following holds.…”
Section: Lower Bound In the Norm Equivalence The Jackson Inequality mentioning
confidence: 78%
“…Before getting to the stability result we remark that the existing perturbation analysis of WHB is one of the primary insights in [34,35]. Although not observed in [34,35], the result does not require substantial modification for locally refined meshes.…”
Section: Lower Bound In the Norm Equivalence The Jackson Inequality mentioning
confidence: 93%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…In Section 3 we discuss another update method that is known as local semiorthogonalization. This approach has been investigated previously in several papers [25,26,34,40,41]. We prove that this update method yields stable one-level wavelet transforms.…”
Section: Introductionmentioning
confidence: 79%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
“…This makes makes HB methods especially ineffective in the 3D local refinement setting. As we mentioned earlier, wavelet-like stabilizations of the HB methods [101] provide a final solution to the condition number growth problem. The motivation for the stabilization hinges on the following idea.…”
Section: Hierarchical Basis Methods and Their Stabilizationsmentioning
confidence: 93%
“…The wavelet modified hierarchical basis (WMHB) methods [101,112,113] can be viewed as an approximation of the wavelet basis stemming from the BPX decomposition [114]. A similar wavelet-like multilevel decomposition approach was taken in [115], where the orthogonal decomposition is formed by a discrete L 2 -equivalent inner product.…”
Section: Hierarchical Basis Methods and Their Stabilizationsmentioning
confidence: 99%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
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