Pith Number

pith:FN4ON4AC

pith:2026:FN4ON4ACBEGQAJB4OB2VG7CK3Y

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A Generalized FC-Gram Approximation Framework with Analysis and Applications

Akash Anand, Prakash Nainwal

A generalized FC-Gram framework adds flexibility to Gram polynomial blending and proves convergence rates of O(n to the minus min of r plus beta and d) for non-periodic functions.

arxiv:2605.04765 v2 · 2026-05-06 · math.NA · cs.NA

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\pithnumber{FN4ON4ACBEGQAJB4OB2VG7CK3Y}

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Record completeness

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4 Citations open

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Claims

C1strongest claim

We establish a convergence theorem showing that the trigonometric interpolant converges at the rate O(n^{-min(r+β,d)}) in the supremum norm on the original interval, where r is the smoothness of the target function, d the number of Gram polynomials, and β ∈ [0,1] a Fourier-decay parameter.

C2weakest assumption

The blending continuation of Gram polynomials can be constructed with the stated flexibility while preserving the controlled boundary behavior and without introducing uncontrolled errors that would invalidate the convergence analysis.

C3one line summary

GenFC generalizes FC-Gram via flexible Gram polynomial blending, proving O(n^{-min(r+β,d)}) convergence and showing better accuracy than prior versions in numerical tests.

Receipt and verification

First computed	2026-06-10T01:10:02.753849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b78e6f002090d00243c7075537c4ade13deae0492263513768974a4f2e6e542

Aliases

arxiv: 2605.04765 · arxiv_version: 2605.04765v2 · doi: 10.48550/arxiv.2605.04765 · pith_short_12: FN4ON4ACBEGQ · pith_short_16: FN4ON4ACBEGQAJB4 · pith_short_8: FN4ON4AC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FN4ON4ACBEGQAJB4OB2VG7CK3Y \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2b78e6f002090d00243c7075537c4ade13deae0492263513768974a4f2e6e542

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fee9ef7aaad0254ca9e14ce59d741cccff1224516b06a069185203fec748d31c",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-06T11:12:36Z",
    "title_canon_sha256": "a8c92f0c79f2f60b3999c0ba09f16e5a2c2c410325c610cff52f03df5af8dcfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04765",
    "kind": "arxiv",
    "version": 2
  }
}