SEARCH · Searcharxiv

Results for “q-fin.RM”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

422 records · Page 4Linked to original sources

arXiv2026

System Identification of Admittance Models for Large Real-World Objects

Simulation of admittance-type models requires physically consistent dynamic models that are rarely available for off-the-shelf, everyday objects, limiting the fidelity of haptic interfaces that rely on such simulations. This paper presents the first complete workflow for producing physically consistent models of large real-world objects with various constraints and mechanisms, guaranteeing physical consistency of inertia and friction parameters. The workflow separates each object and identifies the handle and body in two stages, requiring no torque sensors at hinges, axles, or other constrained joints. Models are produced for a heavy, closer-actuated door and a wheelbarrow, representing objects of differing constraint types and model complexity. The door is modeled using four-bar linkage kinematics and a fluid dynamics-based lumped parameter model including opening, backcheck, swing, and latch zones. The wheelbarrow is modeled as a rigid body with a spherical wheel and no slip during rolling. Handle estimation RMS errors were below 0.64 N and 0.042 Nm across both objects. Door body estimation had RMS error of 2.19 Nm and wheelbarrow body estimation had RMS error of 6.77 Nm.

cs.RO↗

arXiv2026

Patterning in Practice: Debiasing Reward Models with Susceptibilities

Reward models trained on human preferences are known to suffer from length, formatting, and other stylistic biases. In this paper we use patterning, which reweights each preference pair according to its measured effect on posterior expectation values of benchmark losses (its susceptibility), to debias a Gemma 2 9B Instruct reward model trained on Skywork-Reward-Preference v0.2. We obtain $+14.2 \pm 1.2$ pp on RM-Bench Hard, the split where style cues point against correctness (mean $\pm$ s.e.\ over 5 seeds), with overall RM-Bench accuracy preserved, comparable to the strongest Hard-split gain reported by the closest published comparator (SteerRM, $+13.2$ pp). We demonstrate in a simple case that the reweighting is interpretable by tracing a side effect of the intervention (a regression on a safety subset of RM-Bench) to a small class of training pairs, which we confirm by ablation. The weights also transfer: those computed on Gemma 2 9B debias Gemma 2 2B and 27B with no recomputation, and transfer partially to Llama 3.1 8B. This is the first application of patterning, a program grounded in singular learning theory, beyond small models and synthetic tasks.

cs.LG↗

arXiv2026

Proof-Carrying Analytic Approximation: Local-to-Global Evidence Transport at Encoding Cost

Under quasi-uniform refinement, bounded local-encoding hypotheses, and local $W^{r,2}$ approximation of order $r\ge 2$ in a rational piecewise-polynomial presentation of $W^{1,2}(0,1)$, carrying the complete proof genealogy up to the level required by an accuracy $\varepsilon$ costs the same asymptotic bit order as the finest-level conventional coefficient encoding. If $B_n=Θ(M_nβ_n)$ denotes that level-$n$ encoding size, our compiler transports supplied local approximation and overlap witnesses through exact partition-of-unity synthesis and geometric refinement to a represented limit with total certificate size $O(B_{m(\varepsilon)})$, where $m(\varepsilon)=O(\log(1/\varepsilon)/(r-1))$. The construction makes no oracle query to an independently supplied semantic target name ($Q_{\rm target}=0$). When $β_n=O(n+1)$, this becomes $O(\varepsilon^{-1/(r-1)}(1+\log(1/\varepsilon)))$. The surrounding framework is intentionally separated from this resource theorem. Every real computable Banach presentation admits a uniformly computable linear isometric embedding into standard computable $C([0,1])$, with computable inverse on its represented range. Complete metric evidence with rational strict slack collapses extensionally to the represented analytic metric once effective names are available, while chosen evidence transformations retain construction history and resource information. For the Lipschitz grammar used here, qualitative evidence-local lifting is canonical; the nontrivial question is therefore which evidence is retained and at what cost.

math.FA↗

arXiv2026

The Separation of $\mathit{NP}$ and $\mathit{PSPACE}$

There is an important and interesting open question in computational complexity on the relation between the complexity classes $\mathcal{NP}$ and $\mathcal{PSPACE}$. It is a widespread belief that $\mathcal{NP}\ne\mathcal{PSPACE}$. In this paper, we confirm this conjecture affirmatively by showing that there is a language $L_d$ accepted by no polynomial-time nondeterministic Turing machines but accepted by a nondeterministic Turing machine running within space $O(n^k)$ for all $k\in\mathbb{N}_1$. We achieve this by virtue of the prerequisite of $$ {\rm NTIME}[S(n)]\subseteq{\rm DSPACE}[S(n)], $$ and then by diagonalization against all polynomial-time nondeterministic Turing machines via a universal nondeterministic Turing machine $M_0$. We further show that $L_d\in \mathcal{PSPACE}$, which leads to the conclusion $$ \mathcal{NP}\subsetneqq\mathcal{PSPACE}. $$ Our approach is based on standard diagonalization and novel new techniques developed in the author's recent works \cite{Lin21a,Lin21b} with some new refinement.

cs.CC↗

arXiv2026

Landau theory of quenched criticality in linear in-context learning

In-context learning (ICL) allows a pretrained model to infer a new task from examples supplied in its prompt without updating its parameters. In linear models of ICL, the prediction error develops a double-descent singularity when the number of pretraining samples becomes comparable to the number of learnable parameters. We formulate this interpolation singularity as a critical phenomenon of a quenched disordered system. By comparing annealed and quenched descriptions of the same linear ICL model, we identify the connected sample-to-sample fluctuations of the learned parameters as the microscopic origin of the singular error. A Landau potential is constructed by integrating the cavity self-consistency equation for the renormalized ridge parameter $ξ$. The role of (magnetization) order parameter is played by $ξ$, while the bare ridge parameter $λ$ becomes its conjugate magnetic field. The normalized sample complexity $τ$ acts as a temperature and the double-descent singularity occurs at the critical temperature $τ_c =1$. The Landau susceptibility is precisely the quantity that diverges in the fluctuation contribution to the prediction error. The order parameter is closely related to the fraction of zero eigenvalues of the empirical relaxation matrix in the ridgeless limit, which define flat directions in the learning dynamics. The Landau theory is generically cubic in the order parameter with critical exponents $(β_{\rm cr},δ_{\rm cr},γ_{\rm cr})=(1,2,1)$. In the large-context regime, there appears a pseudogap-like regime characterized by suppressed order parameter. Predictions of the Landau theory are independently confirmed from numerical solutions of the original learning problem with good quantitative agreement. Our results pave the way for solid statistical-physics understanding of the interpolation criticality in linear in-context learning.

cond-mat.dis-nn↗

arXiv2026

Mesh-Native Physics-Informed Graph Surrogates for TCAD-in-the-Loop Design Space Exploration

High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.

cs.LG↗

arXiv2026

Adversarial Online Classification with a Preview

Worst-case online classification is governed by sequential complexity, such as Littlestone dimension, and can be impossible even for statistically simple classes, such as thresholds of VC dimension one. We study a preview model in which an oblivious adversary fixes an entire labeled sequence of length $T$, a uniformly random subset of size $pT$ is revealed before prediction begins, and the remaining $(1-p)T$ examples are then presented in their original adversarial order. Against the best full-sequence hypothesis evaluated on the unrevealed examples, we characterize the dependence on the preview rate $p$: for binary classes of VC dimension $d$, the optimal excess loss is $Θ(d/p+\sqrt{dT})$, up to the trivial cap at $T$; for multiclass classes we obtain the corresponding $\widetilde O(d_{\rm DS}/p+\sqrt{d_{\rm Nat}T})$ bound with no dependence on the number of labels. Thus a random preview can replace worst-case sequential complexity by classical statistical dimensions without randomizing the online order. To achieve the sharp binary bound, our ChainedPrediction algorithm uses an online analogue of chaining, implemented as a multiscale aggregation algorithm rather than only as an analytic argument.

cs.LG↗

arXiv2026

FP8 is All You Need (Part 2): Full-FP64 3-D FFT on FP8-Generation Tensor CoresThe Integer-Epilogue Wall and the Minimal Hardware That Would Remove It

The NVIDIA Blackwell Ultra (B300) GPU cuts FP64 vector throughput $\sim 30\times$ while multiplying FP8 tensor throughput. After the recovery of FP64 GEMM via Ozaki Scheme II on FP8 tensor cores and the Tensor-Memory Equilibrium model of the companions ("FP8 is All You Need, Part 1" and "Ozaki 2.5") we ask whether the fifth canonical HPC primitive, the full-FP64 $1024^3$ 3-D FFT, can be carried by the same substrate, and answer with a design and its limit. It is a Bailey six-step transform with no FP64 arithmetic: FP8-tensor DFT GEMMs with fused twiddles, residue-domain Karatsuba combines and exact CRT reconstruction whose bulk is a small GEMM on the FP16 tensor path and whose remainder is a Kulisch fixed-point accumulation with a two-sided modulo-$M$ lift, so the only rounding is the final conversion; constants are machine-generated and verified bit-exactly. The central finding: the binding resource is not floating point but a per-output integer epilogue with floor $(c_{\rm epi}/8),B_{\rm mem}$, $c_{\rm epi} \approx 203$-$281$ instructions per output: on B300 it holds the transform at 63-87 ms against a 12.9 ms roof ($4.9$-$6.7\times$ short); at most $1.3$-$1.9\times$ faster than the collapsed native path, possibly no faster at realised issue rates; no software route reaches the roof; on the NVIDIA Rubin GPU emulation loses $8$-$11\times$. An FP32 variant meets the same wall: the cause is per-scalar reconstruction, not FP64. Each floor term names its remedy: the NVIDIA B200 GPU's INT8 tensor core restored with a position-weighted cross-column accumulation primitive, a load-path deconstruction datapath shared with the companions, two ISA idioms and modular reduction at the MMA output give 16.0-23.5 ms with minor hardware and 12.9-15.0 ms with one moderate ask. All figures are projected floors, not measurements, with sensitivities and the FP8 layout condition given.

cs.MS↗

arXiv2026

BeamRMX: Radiation-Pattern-Driven Learning for Generalizable Beam Radio Map Prediction and Beam Management

The evolution toward sixth-generation (6G) wireless networks is driving larger antenna arrays and highly directional multi-beam transmission, making accurate knowledge of beam-dependent spatial coverage important for beam management and environment-aware network operation. Radio maps (RMs) provide such a representation, yet conventional RM prediction assumes omnidirectional or transmitter-level radiation. In beamformed multiple-input multiple-output (MIMO) systems, one propagation scene instead gives rise to many configuration-dependent beam radio maps (BeamRMs), creating challenges in beam representation and generalization. Existing methods either condition prediction on beam descriptors or use beam maps as auxiliary inputs to generic architectures. We propose BeamRMX, which, to the best of our knowledge, is the first dedicated framework to treat the spatial radiation pattern as the primary BeamRM query and learn how scene geometry transforms it into the received power field. XBase learns multiscale interactions between the radiation query and scene geometry, while an optional Evidence Adapter uses a few cross-configuration BeamRMs from the same scene. Matched-domain and zero-shot experiments show consistent gains over deterministic and diffusion baselines, including mean absolute error reductions of 26.1\% on unseen scenes and 47.8\% on an unseen configuration. Cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

eess.SP↗

arXiv2026

A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

cs.IT↗

arXiv2026

From Symmetry to Capacity: Nested Codes on Binary Memoryless Symmetric Channels

The past decade has seen notable advances in our understanding of structured error-correcting codes, particularly binary Reed-Muller (RM) codes. While initial breakthroughs were for erasure channels based on symmetry, extending these results to the binary symmetric channel (BSC) and other binary memoryless symmetric (BMS) channels required new tools and conditions. Recent work uses nesting to obtain multiple weakly correlated looks at each code bit to establish capacity-achieving performance under bit-MAP and block-MAP decoding. This paper revisits and extends past approaches, aiming to simplify proofs, unify insights, remove unnecessary conditions, and provide new results. By leveraging powerful results from the analysis of boolean functions, we derive recursive bounds using two or three looks at each stage. This gives bounds on the bit-error probability that decay exponentially in the number of stages. For the BSC, we incorporate level-k inequalities and hypercontractive techniques to achieve the faster decay rate required for vanishing block-error probability. The same ideas also extend to product codes with RM component codes, which are transitive but not doubly-transitive in general, and yield vanishing bit-error and block-error probability at rates arbitrarily close to capacity. The results are presented in a semi-tutorial style, providing both theoretical insights and practical implications for future research on structured codes.

cs.IT↗

arXiv2026

Fundamental Limits of Adaptive Beamforming Under Finite Training

Finite training reduces the output signal-to-interference-plus-noise ratio (SINR) of an adaptive beamformer, and a natural question is how much of this loss is unavoidable. This paper determines this question, providing a beamforming counterpart of the Cramér--Rao bound in spectral estimation. An exact identity expresses the SINR loss as a bounded function of the error in the clairvoyant minimum-variance distortionless-response (MVDR) weight. It yields a local asymptotic minimax lower bound over all measurable data-dependent beamforming rules, including biased and irregular rules. The first-order coefficient is $\tr(\Mb\Jb_{\rm eff}^{-1})$, where $\Jb_{\rm eff}$ describes the information in the training data and $\Mb$ measures the sensitivity of the output SINR. Matching constructions determine this coefficient in two complex-Gaussian models. For an $N$-sensor uniform linear array with $K$ distinct point interferers and $2K+1\le N$, a data-driven split one-step beamformer attains the coefficient $C_θ\le K$ at every interior scene of a fixed compact regular parameter set. For unrestricted covariance matrices, sample matrix inversion (SMI) attains the coefficient $N-1$ through the classical Reed--Mallett--Brennan law. The difference quantifies the first-order value of finite-source structure. Geometric formulas and numerical results describe the dependence on interference power and array geometry, and the finite-sample departure near a weak-source boundary.

cs.IT↗

arXiv2026

Sparse Gain Radio Map Reconstruction With Geometry Priors and Uncertainty-Guided Measurement Selection

Radio maps are important for environment-aware wireless communication, network planning, and radio resource optimization. However, dense radio map construction remains challenging when only a limited number of measurements are available, especially in complex urban environments with strong blockages, irregular geometry, and restricted sensing accessibility. Existing methods have explored interpolation, low-rank cartography, deep completion, and channel knowledge map (CKM) construction, but many of these methods insufficiently exploit explicit geometric priors or overlook the value of predictive uncertainty for subsequent sensing. In this paper, we study sparse gain radio map reconstruction from a geometry-aware and active sensing perspective. We first construct \textbf{UrbanRT-RM}, a controllable ray-tracing benchmark with diverse urban layouts, multiple base-station deployments, and multiple sparse sampling modes. We then propose \textbf{GeoUQ-GFNet}, a lightweight network that jointly predicts a dense gain radio map and a spatial uncertainty map from sparse measurements and structured scene priors. The predicted uncertainty is further used to guide active measurement selection under limited sensing budgets. Extensive experiments show that our proposed GeoUQ-GFNet method achieves strong and consistent reconstruction performance across different scenes and transmitter placements generated using UrbanRT-RM. Moreover, uncertainty-guided querying provides more effective reconstruction improvement than non-adaptive sampling under the same additional measurement budget. These results demonstrate the effectiveness of combining geometry-aware learning, uncertainty estimation, and benchmark-driven evaluation for sparse radio map reconstruction in complex urban environments.

cs.CV↗

arXiv2026

Constructions of complete permutations over $\mathbb{F}_q^n$

Complete permutation polynomials play an important role in cryptography, particularly in the design of cryptographic primitives such as the Lai--Massey scheme and S-boxes. We generalize a result of Sun, Li, Guo, and Qu (2021) by characterizing the complete permutation behavior of the mapping $Ψ(X)=M(X+ψ(AX))$ over $\mathbb{F}_q^n$, where $\mathbb{F}_q$ is a finite field of $q$ elements with $q$ being a prime power, $M\in GL(n, \mathbb{F}_q)$, $GL(n, \mathbb{F}_q)$ is the general linear group of order $n$ over $\mathbb{F}_q$, $A_{m \times n}$ is a full-rank matrix over $\mathbb{F}_q$, and $ψ=(ψ_1,ψ_2,\ldots,ψ_n)$ with each component function $ψ_i:\mathbb{F}_q^m\to\mathbb{F}_q$. Furthermore, we establish criteria for the permutation and complete permutation properties of the mapping $F(X)=T(X+B^tf(AX))$ over $\mathbb{F}_{q}^n$, $f: \mathbb{F}_{q}^{m} \rightarrow \mathbb{F}_{q}^{n-m}$, $T \in GL(n, \mathbb{F}_q)$, $A_{m \times n}$ and $B_{(n-m)\times n}$ are full-rank matrices over $\mathbb{F}_q$, $B^t$ represents the transpose of the matrix $B$, and $0<m<n$ are integers. These results also generalize an earlier result of Gravel and Panario (2023), who showed that any arbitrary function $f$ from $\mathbb{F}_q^m$ to $\mathbb{F}_q^{\,n-m}$ can be extended to a bijection over $\mathbb{F}_{q}^n$ through the mapping $F(X)=T(X+B^tf(AX))$, under the condition $AB^t=0$. Here we do not impose the restriction that $AB^t=0$.

cs.CR↗

arXiv2026

Asymptotically Optimal List Size of Random Linear Codes

We prove that for every fixed prime power $q$, every $p\in(0,1-1/q)$, and every $\varepsilon>0$ with $1-H_q(p)-\varepsilon>0$, a random linear code over $\mathbb{F}_q$ of rate $1-H_q(p)-\varepsilon$ is $(p,\,\left\lceil\frac{H_q(p)}{\varepsilon}\right\rceil+O_{p,q}(1))\text{-list-decodable}$ with probability at least $1-q^{-Ω(n)}$. Guruswami, Li, Mosheiff, Resch, Silas, and Wootters showed that, for sufficiently small $\varepsilon$, random linear codes require list size at least $\left\lfloor\frac{H_q(p)}{\varepsilon}+0.99\right\rfloor,$ and conjectured that $\frac{H_q(p)}{\varepsilon}(1+o(1))$ suffices as $\varepsilon\to 0$. This conjecture was previously known for $q=2$, where the upper bound $H_2(p)/\varepsilon+2$ was established. For $q>2$, however, the best known upper bound was $C_{p,q}/\varepsilon$ for a constant $C_{p,q}$ depending on $p$ and $q$. Our result resolves the conjecture for every prime power $q$ and, in fact, establishes the sharper upper bound $\frac{H_q(p)}{\varepsilon}+O_{p,q}(1)$.

cs.IT↗

arXiv2026

Q-VGM: Q-Guided Value-Gradient Matching for Offline-to-Online RL of Flow-Matching VLA

We propose Q-Guided Value-Gradient Matching (Q-VGM), an offline-to-online reinforcement learning (RL) method for fine-tuning flow-matching vision-language-action (VLA) policies with a learned Q-function. Classical off-policy actor-critic methods improve a policy by following the critic gradient $\nabla_A Q$, but applying this update to flow policies requires backpropagation through the multi-step denoising process (BPTT), which is costly and unstable at VLA scale. Existing BPTT-free approaches mostly reduce policy improvement to critic-supervised imitation learning through filtering or reweighting sampled behaviors, or rely on test-time selection and guidance, leaving the underlying policy unchanged. Q-VGM instead formulates policy improvement as optimal control over the denoising dynamics, where the optimal residual velocity is the gradient of a denoising-time value function. Specifically, we train an action-sensitive chunk critic on compact latent states from the frozen VLA backbone, with IQL in the offline phase and TD learning in the online phase. Clean-action estimates improved by iterative Q-gradient ascent are then converted into residual velocity targets that directly supervise the velocity field. Training thus avoids both action-likelihood estimation and the BPTT problem, while requiring no critic at inference time. Starting from a few-shot-SFT $π_{0.5}$ policy on LIBERO, offline Q-VGM improves the average success rate across the Spatial, Object, Goal and Long suites from 84.6% to 90.7% with 150 rollout episodes per task. Offline-to-online training reaches 98.5%, surpassing PPO fine-tuning (97.4%) with approximately $6\times$ fewer rollout episodes. On three real-world bimanual manipulation tasks, offline Q-VGM improves the average success rate from 66.7% to 98.3%.

cs.RO↗

arXiv2026

New upper and lower bounds on covering codes K_q(n,R) for alphabets of size 5 <= q <= 21

Let K_q(n,R) denote the minimum cardinality of a q-ary code of length n with covering radius R. We improve the known bounds on K_q(n,R) in 83 cases (82 distinct cells). On the upper-bound side we give 25 improved bounds for 5<=q<=15 -- twenty-four found by search and one propagated by monotonicity -- using two complementary methods: an engineered focused local search seeded with structural constructions, and a large-neighbourhood search driven by exact full-space coverage transforms that evaluates every candidate codeword position simultaneously. These are, to our knowledge, the first improvements to any upper bound on K_q(n,R) with q >= 5 since the 2011 revision of Keri's tables; several bounds decrease by more than 20%, e.g. K_6(8,4)<=166 (previously 216) and K_8(10,5)<=1883 (previously 2461). On the lower-bound side we give 58 improved bounds for 6<=q<=21, obtained from the semidefinite programming hierarchy of Gijswijt and Polak, whose published results cover q<=5, by combining an exact-arithmetic reimplementation of the reduced program with a multiprecision solution pipeline. Every new lower bound is certified by a rational dual solution validated by a standalone exact-arithmetic checker; no floating-point computation is part of the trusted base. The same pipeline also gives strong numerical evidence of limits: on a dozen further cells the certified value of the relaxation, which the solver reports as optimal to within its working precision, lies below the best known bound, indicating that no improvement is available there at this level of the hierarchy. One cell is improved from both sides: 441<=K_6(10,4)<=2751, previously 417--2952. All codes and certificates are provided in machine-readable form together with standalone verifiers.

math.CO↗

arXiv2024

Convergence of a Ramshaw-Mesina Iteration

In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods and artificial compression methods. Its form makes it an interesting option to replace the pressure update in the Uzawa iteration. The result, for the Stokes problem, is \begin{equation} \left\{ \begin{array} [c]{cc} Step\ 1: & -\triangle u^{n+1}+\nabla p^{n}=f(x),\ {\rm in}\ Ω,\ u^{n+1}|_{\partialΩ}=0,\\ Step\ 2: & p^{n+1}-p^{n}+β\nabla\cdot(u^{n+1}-u^{n})+α^{2}\nabla\cdot u^{n+1}=0. \end{array} \right. \end{equation} For saddle point problems, including Stokes, this iteration converges under a condition similar to the one required for Uzawa iteration.

math.NA↗